Semiconductors (rawat d agreatt)

Presentation by-
Saurav k. Rawat
(Rawat DA Greatt)

Overview
 Introduction
 What are intrinsic semiconductors??
 What are p-type and n-type semiconductors??
 Conductivity of semiconductors
 Mass action law
 Hall effect
 Drift and Diffusion current
 Fermi level in semiconductors
 pn-junction
 Forward Bias & Reverse Bias
 I – V Characteristics of pn-junction
 Applications of semiconductor
 Questions
 References

INTRODUCTION
Solid consist of atoms or molecules which are arranged
in a periodic manner. There is always some basic
arrangement of atoms ,which is repeated throughout the
entire solid material. Such an arrangement of atoms
within a solid is called “CRYSTAL LATTICE “.Such solids
are called “CRYSTALLINE SOLIDS”. Ex- metals and
semiconductor
But there are some solid materials which
don’t have crystalline structure. Such materials are called
“non crystalline or amorphous solids” .Ex-wood , plastic
,paper , glass etc….

Classification of solids
A. Conductors
B. Insulators
C. Semiconductors
A.Conductors:- They have very high electrical conductivity and large
no. of mobile charge carriers or free electrons which carry electric current. When
temperature of conductors increased, its resistivity also increases. They have
positive temperature coefficient of resistance . For eg.. Cu, Ag, Al , Au etc… And
Gold is the best conductor of electricity followed by Cu , Ag & Al.
A good conductor should possess the following characteristics.
i. High electrical and thermal conductivity,
ii. High melting point,
iii. Good oxidation resistance,
iv. Low cost,
v. Good wear and abrasion resistance, and
vi. Better mechanical properties.

(B) Insulators:- Insulators are those
materials which are bad conductors of electivity. i.e, they
have very high resistivity because they have no charge
carriers or free electrons to carry electric current. For eg.
Glass, quartz, rubber, bakelite etc..
(C) Semiconductors:-
semiconductors are those materials whose conductivities
lie between conductors and insulators. They have poor
conductivity than conductors and higher than
insulators. Therefore, they are neither good conductors
nor good insulators. When temp of a semiconductor is
increased, its resistivity decreases or conductivity
increases. At higher temp, a semiconductor conducts
better. Therefore ,the semiconductors have negative
temp coefficient of resistance.

Energy band concept of
Conductor, Insulator and
Semiconductor
Electrical properties of solids are determined by the electrons
in the outermost orbit of an atom. Various electron theories
have been propagated to study the behaviour of solids.
1. Drude-Lorentz (classical) theory,
2. Free electron theory,
3. Energy band theory, and
4. Brilloium zone theory.
whereas the Drude-Lorentz and free electron
theories explain the mechanism of conduction in solids,
energy band theory & Brilloium zone theory explain the
mechanism of semiconductor. The energy band theory also
provides a concept to differentiate between conductors,
semiconductors, insulators.

Free Electron Theory
 The electrons in the outermost orbit are not bound to
its atom, and are to move throughout the solid. These
free electrons are known as “Fermi gas or electron
cloud”. And their potential field remains uniform
throughout the solid due to the ion-cores. The free
electron theory is based on the average potential
energy Ep is a constant throughout the solid, and its
energy difference dEp=0. so the total energy E is equal
to the kinetic energy Ek only.

Free electron theory
The kinetic energy is given by
퐸 =
ℎ2푛2
8푚푙2
Where-h=
Plank’s constant,
n= Principle quantum no.
m= Mass of free electron
l= Length of the solid.
Where –
푙 = ±푛휋/푘
where
k= the wave number.
this eq. is true in the case of
unidirectional flow of electrons.
A plot between kinetic energy Ek and
wave no. 푘 = 2휋/휆
휆=De-Broglie’s wavelength
Ek
-k 0 +k
Wave number

Energy band theory
Potential energy of an electron is a function of its position with respect to
the ion-cores. Considering Heisenberg’s uncertainty principle and Bragg’s
diffraction pattern of electrons, the potential of an electron can’t be
neglected as compared to its dimension. This is due to the “standing
wave” of an electron gives rise to a periodic variation in its amplitude. The
probability of finding electron remains max. at the crest of the waveform.
The two possible waveforms are sine wave and cosine wave , formed due
to superimposition of ‘travelling’ de Broglie waves. These waveforms
satisfy Bragg’s law
2푑 sin 휃 = nλ
The potential energy can’t be assumed to zero, and the energy will be
given by
E=Ek+Ep
At critical conditions of 푘 = ±푛휋/푑 for n=1,2,3,4………..etc., the
electron is described by a standing wave . When the waveforms are either
sine or cosine type, the potential energy shows deviations.

Energy band theory
 This deviations results in
break of E vs k curve,
giving rise to an energy
gap. This energy gap Eg is
between different orbits
K,L,M….etc. .
of an electron
.
 Magnitude of this energy
gap is an indication of the
difference in potential
energy for electron
locations of two different
waveforms. The two
closely spaced energy
levels as known as energy
bands.

semiconductor
 Electrical properties lie between insulators and good conductors.
 At room temp, they have conductivity lower than conductors and
higher than insulators.
 Their resistances decreases with the increase in temp. therefore they
have negative temp coefficient of resistance.
 Conductivity lies between the range of 105 to 10-4 siemens/meter.
 Their resistivity or conductivity changes when even a very small amt. of
certain other substances called impurities, are added to them.
 Semiconductors are two types,
 Elemental semiconductors, for eg Ge and Si,
 Compound semiconductor , for eg GaAs.
 Semiconductors may also be classified in following way:
 Intrinsic semiconductor
 Extrinsic semiconductor

INTRINSIC SEMICONDUCTOR
 A semiconductor in an extremely pure form is known as
“intrinsic semiconductor”.
 The structure has zero overall charge
 At a low temp. such as absolute zero (0K),all the valence
electrons as tightly held by parent atoms and by
covalent bonds with other atoms. Electrons can’t move
through the crystal.
 No free electrons are available to conduct electricity. So
at T=0K they behaves as an insulators.
 Two-dimensional representation of the silicon crystal.
The circles represent the inner core of silicon atoms,
with +4 indicating its positive charge of +4q, which is
neutralized by the charge of the four valence electrons.
Observe how the covalent bonds are formed by sharing
of the valence electrons. At 0 K, all bonds are intact and
no free electrons are available for current conduction.

Generation of electron- hole
pairs  The temp increased up to room temp
(300K), some covalent bonds break and
electron becomes free to move through
the c crystal.
 A vacancy is also produced and called as
a “Hole”.
 When a free electron is produced, a
hole is also produced simultaneously.
i.e, electrons and holes are produced in
pairs and is called “electron-hole pair” .
 The concentration of free electrons will
always equal to the concentration of
holes.
 The generation of electrons and holes
due to temp is called “Thermal
generation”.
 At room temp, they have some
conductivity.
 Electron is a negatively charged particle
and hole is positively charged particle.
 Electrons and holes is called “free
charge carriers”.

 To break a covalent bond in the crystal
lattice, a certain amount of energy is
required. For eg. Energy for Ge is
0.72eV and energy for Si is 1.12eV.
 The holes remains in valence band and
electron lifts to conduction band to
take part in conduction of current.
 The energy to lift the electron from
valence band to conduction band is
0.72eV for Ge and 1.12 eV for Si.
 Recombination
 There is a possibility of collision
between electrons and holes.
 In collision, an electron takes the
position of holes and both of them
disappear and this process is called
recombination.
 Energy released as a quantum heat or
light .

 Quantum is absorbed by another electron to breakaway
from its valence band and creates a new electron-hole pair.
 At given temp, the rate of generation of electrons and holes
is equal to rate of combination.
Effect of temp on conductivity of intrinsic semiconductor
 Semiconductor ( Ge or Si) acts as a perfect insulator at
absolute zero.
 At room temp (300K) some electron-hole pairs are
produced due to thermal energy. For eg. In Ge,
concentration of free electrons or holes is 2.5 ×1019/m3 at
300 K. i.e, they have small conductivity.
 The temp is raised further, more electron-hole pairs are
produced.
 At higher temp, the conc. Of charge carriers will be higher.
 So, the conductivity of intrinsic semiconductor increases
with temp. i.e, resistivity decreases with increases in temp.
 Semiconductor has “negative temp-coefficient” of
resistance.

Extrinsic semiconductor
 Pure semiconductor have small conductivity at room temp.
therefore they are not of much use.
 By adding some amount of impurity atoms to a pure
semiconductor, we can change its conductivity or
characteristics.
 The process of adding impurity to a pure semiconductor is
called “doping”.
 Doping is done at a rate such that only one atom of
impurity is added per 106 to 1010 semiconductor atoms.
 On adding impurities, either the no. of electrons or holes
increases.
 A doped semiconductor is called “extrinsic
semiconductor”.
 Types of extrinsic semiconductors,
 N – type semiconductor
 P – type semiconductor

N- type semiconductor
• The Pentavalent impurity atoms are added to a
pure semiconductor, “ N-type semiconductor” is
obtained.
• The pentavalent impurity atom has five outer
(valence) electrons, rather than the four of silicon.
• The size of the pentavalent atoms is roughly same
as that of Si or Ge. For eg. P, Sb, As, etc….
• The amount of impurity is very small, it is
assumed that each impurity atom is surrounded
by Si atoms.
• The phosphorus atom has five valence electron.
Only four of the valence electrons are required for
covalent bonding.
• The fifth electron has no chance of forming a
covalent bond.
• The fifth is much more easily detached from the
parent atom.

 The fifth is much more easily detached from the parent atom .
 A very little amount of energy is required to deattach
this electron from the nucleus of its parent atom.
 The energy needed to free the fifth electron is smaller
than the thermal energy at room temperature virtually all are freed.
 The energy for Si and Ge are 0.05eV and 0.01 eV .
 Each impurity atom donates one electron to the conduction band,
therefore pentavalent impurity is called “Donor type impurity”.
 Large number of donated electrons , there are also some thermally
generated electron-hole pairs.
• Large number of electrons increases the rate of recombination of
electrons with holes.
• The net concentration of holes is much less than intrinsic value.
• N – type semiconductor is also called “ donor ion”
• The donor ion is held and is called positively charged “ immobile ion”.
• Electrons are in majority carriers.

N – type semiconductor
• Holes are in minority carriers
• It has large number of immobile positive ions.
• N – type semiconductor is not negatively charged but
they are electrically neutral.
• The total number of electrons is equal to the total number
of holes and immobile ions.
The negative charge is exactly balanced by the positive
charge.

P- type semiconductor
 The trivalent impurity atoms are added to
the pure semiconductor , p-type
semiconductor.
 The trivalent impurity atoms have three
electrons in the valence shell.
 The size of the trivalent atoms is roughly
same as that of Si or Ge. eg. B , Al , Ga , In
etc…..
 The amount of impurity is very small, it is
assumed that each impurity atom is
surrounded by Si atoms.
 the doping atom has only three electrons
in its outer shell i.e, In
 The impurity atom ( In ) is surrounded by
silicon atoms.
 These three electrons form covalent bonds
with the three neighbouring silicon atoms.

P - t y p e s emi c o n d u c t o r
 The fourth silicon atom can not make a covalent bond with the
Indium atom because the indium atom does not have fourth
valence electron.
 The fourth covalent bond is incomplete.
 A vacancy that exists in the incomplete covalent bond
constitutes a hole.
 The hole has a tendency to complete the covalent bond from the
neighbouring atoms to complete the covalent bond.
 An electron from neighbouring atoms require some energy to
jump into the vacancy.
 At room temperature , this small amount of energy is provided
by thermal energy. For eg, the energy for Si and Ge is 0.05 eV and
0.01 eV respectively .
 When an electron from the neighbouring atoms jump into the
vacancy around the Indium atom to complete the covalent
bonds, the effect is two fold.

I. Another hole or vacancy is created in the covalent
bond of surrounding atom from where the electron
had jumped.
II. After acquiring an electron , the Indium atom
becomes a negative ion.
 The Indium atom accepts one electron to become
negative ion , it is also called “ Acceptor ion or
Acceptor type impurity”.
 The negative ion is “immobile” because it is held in the
crystal structure by covalent bonds.

 The large no. of holes are created due to acceptor type
impurities .
 The large no. of holes increases the rate of
recombination of holes with electrons so that no. of
electrons is further reduced then intrinsic level .
 In P-type semiconductors , holes are the majority
carriers and electrons are the minority carriers .
 The P-type materials has holes as majority carriers
electrons as minority carriers and
negative mobile ions .
 They have two type of charge carriers and immobile
negative ions .

Effect of temperature on extrinsic
semiconductor
 The addition of small amount of donor or acceptor impurity generate a
large no. of charge carriers in any extrinsic semiconductors .
 Due to this large no. of charge carriers ,the conductivity of an extrinsic
semiconductors is several times that of an intrinsic semiconductors at
room temperature (300k).
 All the donor atoms have already donated there free electrons (at 300 k),
the additional thermal energy due to energy in temperature only serves to
increase the thermal produced carriers .
 The concentration of minority carriers increases.
 When the temperature is reached , the number of covalent bonds broken
is quite large i.e , the number of holes is nearly equal to the number of
electrons.
 The extrinsic semiconductor now acts like an intrinsic semiconductor with
higher conductivity.
 The critical temperature for Si and Ge is 2000 C and 850 C .

Conductivity of metals
 The conductivity of a material is proportional to the of free electrons.
 A constant electric field E is applied to the metal , the free electron
would be accelerated and the velocity would increase indefinitely with
time.
 Electrons loss energy because collision of electrons.
 A steady-state conduction is reached where a finite value of drift
velocity Vd is attained.
 The drift velocity Vd is opposite of the electric field and its magnitude
is proportional to E.
………. (1)
v E drift  
= The mobility of electrons in m2/volt-second


conductivity of metal
Due to the applied electric field , a steady-state drift velocity has been
superimposed upon the random thermal motion of the electrons. Such a directed
flow of electrons constitutes current.
If the concentration of free electrons is n ( electrons/m3 ) ,the
current density J ( ampere/m2) is…
J=nqVd …………….(2)
From eq. (1)
where,
J  nqE
J E
  nq
= The conductivity of metal in (ohm-metre)-1


Conductivity of
intrinsic semiconductor
Intrinsic semiconductors behave as perfect insulator at 0K. Because at 0K,
the valence band remains full, the conduction band empty and no free
charge carriers for conduction. But at room temperature (300K) , the
thermal energy is sufficient to create a large number of electron-hole pairs.
Now if an electric field is applied, the current flows through the
semiconductor. The current flows in the semiconductor due to the
movement of electrons in one direction and holes in opposite direction.
so, the current density of a metal is..
……………….(1)
J  nqE
The current density in a pure semiconductor , due to the movement of
electrons and holes is given by….
…………………..(2)
J qn E n n  
J qp E p p  
where- ………………....(3)
q= the charge on electron or hole
n= electrons concentration

p= holes concentration
E= applied electric field
= mobility of electrons
= mobility of holes
The total current density will be,
J = Jn+Jp ……………(4)
From eqn.(2) & (3), we get
…………(5)
…………(6)
J  qnnE  qppE
J  qE(nin  nip)
Where- …………(7)
E J  
= the conductivity of semiconductor
For pure semiconductor, the number of electrons is equal to the
number of holes. i.e, n=p=ni
ni= intrinsic carrier concentration
So eqn. (6) will be,
……….(8)
n 
p
  (nn  pp)q

J  qE(nin  nip)

The conductivity of pure semiconductor will be
) ( p i n i nnq
  qni(n p)
The conductivity of pure semiconductor depends upon its
intrinsic semiconductor , mobility of electrons and holes.
Conductivity of N-type and P-type Semiconductor
The conductivity of an intrinsic semiconductor is given by
  q(nin  nip)
Putting n=p=ni
For N-type semiconductor
n>>>p
J n 
qn 
n
E
J p 
qn 
p
E
So , the conductivity of n-type semiconductor
  qnn
For P-type semiconductor
p>>>n
So, the conductivity of P-type semiconductor
  qpp

Mass-Action law
When a pure semiconductor is doped with N-type impurities, the
number of electrons in the conduction band increases above a level and
the number of holes in the valence band decreases below a level which
would have been available in the pure semiconductor. Similarly, if the P-type
impurities are added to a pure semiconductor ,the number of holes
increases in the valence band above a level and the number of electrons
decreases below a level which would have been available in the pure
semiconductor.
Under thermal equilibrium for any semiconductor , the
product of the number of holes and the number of electrons is constant
and is independent of the amount of donor and acceptor impurity doping.
Mathematically,
2
n.p=ni
Where,
n= the number of free electrons per unit volume,
p= the number of holes per unit volume, and
ni= the intrinsic concentration.

HALL EFFECT
If a specimen ( metal or semiconductor ) carrying a
current I is placed in a transverse magnetic field (B) then
an electric field is induced in the direction of
perpendicular to both I & B.
Hall effect application :-
 To determine whether a semiconductor is N-type or P-type.
 To determine carrier concentration.
 To measure the conductivity of a material and then
compute mobility.

+
+ + + +
i
B
P
Q
X
Y
Z
V + + + + + H
+ + + + + + +
+ + + + + + +
+
-
P – type semiconductor

i
B
X
Y
Z
-
VH
+
_ _
_ _ _
_
_ _
_
_ _ _ _
_
_
_
_ _ P
Q
N – type semiconductor

Drift current
If an electric field is applied across the semiconductor, the charge carriers
attain a drift velocity Vd. “The drift velocity Vd is equal to the product of the
mobility of charge carriers and the applied electric field intensity (E)”.
The holes move towards the negative terminal of the battery and
electron moves towards the positive terminal of the battery. This
combined effect of movement of the charge carriers constitutes a current
known as the “ drift current”.
The drift current density due to the charge carriers such as the free
electrons and holes are the current passing through an area perpendicular
to the direction of flow.
The drift current density, Jn due to free electrons is given as
Jn=푞푛 휇n E
The drift current density, Jp due to holes is given as
Jp=푞푛 휇p E

Where –
n= electron concentration
p= hole concentration
E= applied electric field
q= electronic charge
= mobility of electrons
= mobility of holes
n 
p

Diffusion & Diffusion current
An electric current flows in a semiconductor even in the absence of
an applied voltage, if a concentration gradient exists in the
material. A concentration gradient exists when the number of
either electrons or holes is greater in one region of a semiconductor
as compared to the rest of the region.
If the concentration gradient of charge carriers exists in a
material, the carriers tend to move from the region of higher
concentration to the region of lower concentration. This process is
called “Diffusion”. And the electric current due to this process is
known as “ Diffusion current”.
Let us consider, a piece of semiconductor in which the
concentration of free electrons (n) is not uniform. Also let
concentration of electrons be non-uniform in the x-direction.
The rate of change of concentration or concentration
gradient is dn/dx.
The concentration of electrons is changing with x, the
density of electrons in one site is more than the density in the other
side. Electrons are free to move from the greater concentration side
to the lower concentration side.

Diffusion & Diffusion current
The diffusion current density Jn for
electrons is proportional to the
concentration gradient.
jn∝
푑푛
푑푥
Or Jn= 푞퐷푛
푑푛
푑푥
The diffusion current density Jp for holes,
Jp= −푞퐷푝
푑푛
푑푥
where-
Dp & Dn= Diffusion constant for
holes and electrons
q= charge of an electrons
The negative sign shows that
푑푛
푑푥
is
negative when the charge density falls
with increase of x.

Energy band diagram for
intrinsic semiconductor
Conduction
band
Valence band
EG
EC
EV
Forbidden
energy gap

Fermi level in an Intrinsic
semiconductor
“The energy state or level which has a 50 % probability of
being filled by an electron.”
For intrinsic semiconductor, the fermi level lies midway
between conduction band and valence band.
At an absolute temperature (0 k), all energy states
above the fermi level are empty and all energy states below
the fermi level are occupied or filled up. As temp increases,
some covalent bonds break up and such electrons go to the
conduction band . Due to this , the fermi level shifts upward
as the temp increases.

Fermi level in an Intrinsic
semiconductor
Conduction
band
Valence band
EF
EC
EV
Fermi level

Let at any temp T K
Number of electrons in the conduction band = nc
Number of electrons in the valence band = nv
Total number of electrons in both band, n=nc+nv ……(A)
For simplification let us assume that
I. widths of energy bands are small in comparison to forbidden energy gap
between them
II. All levels in band have the same energy , bandwidths being assumed to
be small
III. Energies of all levels in the valence band are E0 ,
IV. Energies of all levels in conduction band are EG.
Let the zero-energy reference level be taken arbitrarily at the top of the
valence band ,
Now number of electrons in conduction band , nc=n.P(EG) ……(1)
Where,
P(EG)= the probability of an electron having energy EG.
From Fermi-Dirac probability distribution function ,
1
푃 퐸 = …….(2)
1 + 푒(퐸−퐸퐹)/푘푇

Where P(E) is the probability of finding an electron having energy E.
푃 퐸퐺 =
1
1 + 푒(퐸퐺−퐸퐹)/푘푇
Putting the value of P(E) in eqn (1), we get
nc=
푛
1+푒(퐸퐺−퐸퐹)/푘푇 …………(3)
Now number of electrons in the valence band ,
nV=n.P(0) …………(4)
The probability P(0) of an electron in the valence band with zero-energy, E=O ,
then eqn(2) will be
푃 0 =
1
1 + 푒(표−퐸퐹)/푘푇 =
1
1 + 푒−퐸퐹/푘푇
Putting the value of P(0) in eqn (4) , we get
nv=
푛
1+푒(−퐸퐹)/푘푇 …………..(5)
Putting of the values of nc and nV in equation (A) and we get,
n= nc+ nv=
푛
1+푒(퐸퐺−퐸퐹)/푘푇 +
푛
1+푒(−퐸퐹)/푘푇
1=
1
1+푒(퐸퐺−퐸퐹)/푘푇 +
1
1+푒(−퐸퐹)/푘푇
1-
1
1+푒(−퐸퐹)/푘푇 =
1
1+푒(퐸퐺−퐸퐹)/푘푇
After simplification,
EF =
1
2
EG

Energy band diagram for n- type
semiconductor
n –type semiconductors are
obtained by adding donor type or
pentavalent impurities to pure
semiconductors. The energy level
of donor atoms is slightly below the
conduction band. This donor
energy level is only 0.01 eV below Ec
level in Ge and 0.05 eV below Ec
level in Si. This small amount of
energy is provided to the electrons
of the donors, then the fifth
electron of the atom is raised to the
conduction band and takes part in
conduction electric current.
Actually , at room temperature, this
small amount of energy is supplied
to the electrons .
Conduction
band
Valence band
Energy
level of
donor ED
EC
EG
EV
0.01 ev
for Ge
& 0.05
ev for
Si

Energy band diagram for p- type
semiconductor
p –type semiconductors are
obtained by adding acceptor type or
trivalent impurities to pure
semiconductors. The energy level of
acceptor atoms is slightly above the
valence band. This donor energy
level is only 0.01 eV above Ev level in
Ge and 0.05 eV above EV level in Si .
This small amount of energy is
provided to the electrons of the
acceptor, then they are able to leave
the valence band and reach the
acceptor energy level, the electron
fill up the fourth covalent bond . In
this process, an electron which
leaves the valence band creates a
hole in the valence band.
Conduction
band
Valence band
EG
Energy
level of
acceptor
EA
0.01 ev
for Ge
& 0.05
ev for
Si
EC
EV

Fermi level in an n – type
semiconductor
The number of electrons increases in the
conduction band because of donor
impurities. Due to this , the fermi level
shifts upward closer to the conduction
band.
For n – type semiconductor , the fermi
level EF may be expressed as
Where-
EF = fermi level
k = Boltzman’s constant
n
(1.38× 10-23 joule/ 0K)
T= temperature in K
nC = No. of electrons in conduction band
EC= Energy level of conduction band
ND= concentration of donor impurity.
Conduction
band
Valence band
EC
EF
EV
ED
Donor level
Fermi
level
D
F C
N
E E kT
C
  .log

Fermi level in an p – type
semiconductor
The number of electrons decreases in the
conduction band because of acceptor
impurities. Due to this , the fermi level
shifts downward closer to the valence
band.
For p– type semiconductor , the fermi
level EF may be expressed as
Where-
EF = fermi level
n
k = Boltzman’s constant
EV= Energy level of valence band
T= Temperature in K
nV = Number of electrons in valence band
NA= concentration of acceptor impurity.
Conduction
band
Valence band
EC
EF
EV
EA
Acceptor
level
Fermi
level A
F V
N
E E kT
V
  .log

p-n junction
 A piece of p –type semiconductor is joined to a piece of n – type
semiconductor in such a manner that the crystal structure remains
continuous at the boundary, then “p-n junction” is formed.
 To form p-n junction, a special fabrication techniques are required.
 A wafer of the semiconductor material is doped so that one region is n-type
and the other region is p-type.
p-n
junction
P N

The depletion region formation
The p- region contains –
 Holes as majority carriers,
 Electrons as minority carriers ,
 Acceptor ions ( i.e, negative charged immobile ions )
The n-region contains –
 Electrons as majority carriers,
 Holes as minority carriers,
 Donor ions ( i.e, positive charged immobile ions )
Therefore , the hole sample is neutral.
No voltage is applied to the p-n junction, as soon as the p-n junction is
formed. The following actions take place;
 Holes from the p-region diffuse into the n-region and they combine
with the electrons in the n-region.
 Electrons from the n-region diffuse into the p-region and they
combine with the holes in the p-region.

 P-region has more number of holes and n-region has more
number of electrons. Therefore , there is a difference of
concentrations in two regions.
Due to this difference , the diffusion of holes and electrons
takes place.
A concentration gradient is produced due to the difference
concentration.
 The electrons and holes move at random in all directions
because of thermal energy.
Some charge carriers cross the junction.
 The process of diffusion continues only for a short period of
time.
A restraining force is set up automatically in the
neighbourhood of the junction , after few recombination of
electrons and holes. This restraining force is called “Barrier”.

The formation of this barrier
may be given in following steps :-
As the p-n junction is formed,
some of holes in the p- region
and some of the electrons in the
n- region diffuse in each other
and recombine.
Each recombination eliminates
a hole and a free electron.
The negative acceptor ions in
the p-region and positive donor
ions in the n-region are left
uncovered or uncompensated in
the neighbourhood of the
junction.
Depletion region

 Holes trying to diffuse into n- region are repelled by
the uncovered positive charge of the donor ions.
Similarly, electrons trying to diffuse into p- region are
repelled by the uncovered negative charge of the
acceptor ions.
 Due to this , further diffusion of holes and electrons
across the junction is stopped.
The region having uncompensated acceptor and donor
ions is called “depletion region”.
This depletion region is also called “space-charge
region”
The width of depletion region depends upon the
doping level of impurity in n-type and p-type
semiconductor.
The greater the doping level, the depletion region will
be thinner.

Potential barrier for a pn-junction
 The electric field between the acceptor and the donor
ions is called a barrier.
 The width of the barrier is the physical distance from
one side of the barrier to the other side .
 The height of the barrier = The difference of
potential from one side of the barrier to the other
side.

pn Junction Under Open-Circuit
Condition
Fig (a) shows the pn junction
with no applied voltage (open-circuited
terminals).
Fig.(b) shows the potential
distribution along an axis
perpendicular to the junction.

Biasing of a pn-junction
 When we apply a battery across the pn-junction, this
process is called “Biasing of a pn-junction”.
 The width of the depletion region can be controlled by
applying external voltage source across the
pn-junction.
 The pn-junction can be biasing in two ways :
I. Forward-Bias
II. Reverse-Bias

The pn Junction Under Forward-
Bias Conditions
Conventional
Current Flow
I (Forward)
Moving
electrons
Small dynamic
resistance
+ -
 Positive terminal of the
battery is connected to the
p-side and the negative
terminal to the n-side.
Holes are repelled from the
positive terminal of the
battery and forced towards
the junction.
 Electrons are repelled from
the negative terminal of
the battery and forced
towards the junction.

 Because of this increased energy , some holes and electrons
enter the depletion region. This reduces the potential
barrier.
Resistance of device decreases.
 For each recombination of free electron and hole, an
electron from the negative terminal of the battery enters
the n-type region and then moves towards the junction.
 In the p-type region near the positive terminal of the
battery, an electron breaks a bond in the crystal structure
and enters the positive terminal of the battery.
 For each electron which breaks its bond, a hole is created.
Hole move towards to the junction.
 The current through the external circuit is due to the
movements of electrons only.
 The current in the p-type region is due to the movements
of holes.
 The current in the n-type region is due to the movements
of electrons.

The pn Junction Under Reverse-
Bias Conditions
Moving
Electrons
in reverse
large dynamic
resistance
- +
 Positive terminal of the
battery is connected to the
n-side and the negative
terminal to the p-side.
Holes in the p-region are
attracted towards the
negative terminal of the
battery.
 Electrons in the n-region
are attracted towards the
positive terminal of the
battery.

 Majority charge carriers are drawn away from the pn-junction.
 The depletion region becomes wider and increases the barrier
potential.
 Due to this, the majority charge carriers are not able to cross the
junction.
 There is no current due to the majority charge carriers.
 There are few thermally generated minority carriers in both the
regions.
 The increased barrier potential enhances the flow of the
minority carriers across the junction.
 The generation of the minority carriers depends upon the
temperature and independent of the reverse voltage applied.
 When the temperature is constant, the current due to the
minority carriers also remains constant whether the reverse bias
voltage is increased or decreased. Therefore , due to this region ,
the current is called “ reverse saturation current”.
 The reverse saturation current is order of microamperes (휇퐴) for
Ge pn-junction and nanoamperes (nA) for Si pn-junction.

P-N Junction - V-I characteristics
Voltage-Current relationship for a p-n junction (diode)

Current-Voltage Characteristics
THE IDEAL DIODE
Positive voltage yields finite
current
Negative voltage yields
zero current
REAL DIODE

Applications of semiconductor
devices
Semiconductor devices are all around us. . They can be found in
just about every commercial product we touch, from the family car
to the pocket calculator.
 Rectifiers which are used in d. c. power supplies.
 Wave shaping circuits such as clippers and clampers.
 Voltage regulator circuits.
 Portable Radios and TV receivers.
 Science and industry,
 solid-state devices, space systems, computers, and data
processing equipment,
 military equipment,
 Data display systems, data processing units, computers, and
aircraft guidance-control assemblies etc…

Review questions
Section – A
1) In n- type semiconductors electrons are the …………….. carriers.
2) Silicon doped with Arsenic is an example of ……………………….
3) The addition of small amount of impurity to a semiconductor
before it crystallises is called ……………
4) Free Electron theory of metals was proposed by ......................
5) A ………………………. is that material whose electrical properties lie
between those of insulator and …………………….
6) Impurity added to a semiconductor is known as …………… agent.
Section – B
1) Discuss p-n junctions.
2) Explain intrinsic and extrinsic semiconductors.
3) Explain Band theory in metals.

Section - C
1) What are semiconductors ? Discuss the intrinsic
semiconductors.
2) Using the “ Band theory of metal ” differentiate between a
metal , an insulator and a semiconductor.
3) What are Semiconductors ? How will are they classified ?
Discuss them in detail.
4) What are Insulators and semiconductors ? Explain the
classification of semiconductors and discuss in detail.
5) Write a note on the following :
Band theory and Band structure of metals.
Intrinsic and extrinsic semiconductors.
Doping semiconductors.

References
1) SANJAY SHARMA ‘Basic Electronics’ S. K. Kataria &
Sons , Delhi , 2004
2) K. M. GUPTA , ‘Material Science and Engineering’
Umesh Publications, Delhi, 2002
3) J. B. GUPTA , ‘Electronics Engineering’ S. K. Kataria
& Sons , Delhi , 2010
4) B. K. SHARMA, ‘Engineering Chemistry’ Krishna
Prakashan Media ( P ) Ltd., Meerut, 2005
5) H. V. KEER, ‘Principles of the Solid State’ new age
International ( P ) Ltd., New Delhi , 2008

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