Classification of materials-metals (conductor), semiconductor,

Insulator:

On the basis of electrical conductivity(σ) or resistivity (ρ=1/σ) solids

can be broadly classified as

1. Metal or conductors: They possess low resistivity (ρ) or high

conductivity(σ)
ρ~10-2- 10-8 Ωm
σ~102- 108 Ω-1 m-1 (Ω-1=S)
2. Semiconductors: They posses resistivity (ρ) intermediate of
metals and insulators
ρ~10-5- 10-6 Ωm
σ~105- 106 Ω-1 m-1
3. Insulators: They possess high resistivity (ρ) or low
conductivity(σ)
ρ~1011- 106 Ωm
σ~10-11- 10-6 Ω-1 m-1

Classification of material on the basis of energy band gap:

➢ Energy band: The possible energies of the electrons of an
atom are generally represented by energy levels. When
several atoms are brought together to form a solid crystal,
the outer electrons of the various atoms interact with each
other and form closely spaced energy levels called energy
bands.
 ➢ Valance band: the lower completely filled energy band of
valence electrons is called valance band (VB)
➢ Conduction band: The upper unfilled energy band of
conduction electrons above the VB is called conduction
band (CB)
➢ Forbidden gap (Eg): The energy gap between the top of the
valence band and bottom of the conduction band is called
the energy band gap or forbidden gap.

Depending upon the value of Eg material can be classified into three

types

1. Metal or conductors: Eg≈0, valance band and conduction band

overlap.
2. Semiconductors: Eg<3ev,
For Ge, Eg=0.67ev,
For Si, Eg=1.1ev,

3. Insulators: Eg>3ev,
For diamond Eg≈6ev,

Semiconductors can be classified as:

• Intrinsic Semiconductor
• Extrinsic Semiconductor

Classification of Semiconductors

Intrinsic Semiconductor
An intrinsic type of semiconductor material is made to be very pure
chemically. It is made up of only a single type of element.
 Conduction Mechanism in Case of Intrinsic Semiconductors (a) In
absence of electric field (b) In presence of electric Field
Germanium (Ge) and Silicon (Si) are the most common type
of intrinsic semiconductor elements. They have four valence
electrons (tetravalent).
They are bound to the atom by covalent bond at absolute zero
temperature.
When the temperature rises, due to collisions, few electrons are
unbounded and become free to move through the lattice, thus
creating an absence in its original position (hole). These free
electrons and holes contribute to the conduction of electricity in the
semiconductor. The negative and positive charge carriers are equal
in number.
The thermal energy is capable of ionizing a few atoms in the lattice,
and hence their conductivity is less.

➢ Hole: It is the positive entity of electron vacancy which is

produced when electrons jump from VB to CB.

The Lattice of Pure Silicon Semiconductor at Different Temperatures

 • At absolute zero Kelvin temperature: At this temperature,
the covalent bonds are very strong and there are no free
electrons and the semiconductor behaves as a perfect
insulator.
• Above absolute temperature: With the increase in temperature
few valence electrons jump into the conduction band and hence
it behaves like a conductor.

Energy Band Diagram of Intrinsic Semiconductor

The energy band diagram of an intrinsic semiconductor is shown
below:

(a) Intrinsic Semiconductor at T = 0 Kelvin, behaves like an insulator

(b) At t>0, four thermally generated electron pairs
In intrinsic semiconductors, current flows due to the motion of free
electrons as well as holes. The total current is the sum of the
electron current Ie due to thermally generated electrons and the hole
current Ih
Total Current (I) = Ie + Ih
For an intrinsic semiconductor, at finite temperature, the probability
of electrons to exist in conduction band decreases exponentially
with increasing bandgap (Eg)
n = n0e-Eg/2.Kb.T
Where,

• Eg = Energy bandgap
• Kb = Boltzmann’s constants

Extrinsic Semiconductor
The conductivity of semiconductors can be greatly improved by
introducing a small number of suitable replacement atoms called
IMPURITIES. The process of adding impurity atoms to the pure
semiconductor is called DOPING and the impurity is called dopant.
Usually, only 1 atom in 107 is replaced by a dopant atom in the doped
semiconductor. An extrinsic semiconductor can be further classified
into:

• N-type Semiconductor
• P-type Semiconductor
 Classification of Extrinsic Semiconductor

N-Type Semiconductor

• Mainly due to electrons

• Entirely neutral
•

• Majority – Electrons and Minority – Holes

When a pure semiconductor (Silicon or Germanium) is doped by
pentavalent impurity (P, As, Sb, Bi) then, four electrons out of five
valence electrons bonds with the four electrons of Ge or Si.
The fifth electron of the dopant is set free. Thus, the impurity atom
donates a free electron for conduction in the lattice and is called
“Donar”.
Since the number of free electron increases by the addition of an
impurity, the negative charge carriers increase. Hence, it is called n-
type semiconductor.
Crystal as a whole is neutral, but the donor atom becomes an
immobile positive ion. As conduction is due to a large number of free
electrons, the electrons in the n-type semiconductor are the
MAJORITY CARRIERS and holes are the MINORITY CARRIERS.

P-Type Semiconductor

• Mainly due to holes

• Entirely neutral
• I = Ih and nh >> ne
• Majority – Holes and Minority – Electrons
When a pure semiconductor is doped with a trivalent impurity (B, Al,
In, Ga ) then, the three valence electrons of the impurity bonds with
three of the four valence electrons of the semiconductor.
This leaves an absence of electron (hole) in the impurity. These
impurity atoms which are ready to accept bonded electrons are
called “Acceptors“.
With the increase in the number of impurities, holes (the positive
charge carriers) are increased. Hence, it is called p-type
semiconductor.
Crystal as a whole is neutral, but the acceptors become an immobile
negative ion. As conduction is due to a large number of holes, the
holes in the p-type semiconductor are MAJORITY CARRIERS and
electrons are MINORITY CARRIERS.
Difference Between Intrinsic and Extrinsic Semiconductors

Intrinsic Semiconductor Extrinsic Semiconductor

Pure semiconductor Impure semiconductor

Density of electrons is equal Density of electrons is not equal

to the density of holes to the density of holes

Electrical conductivity is low Electrical conductivity is high

Dependence on temperature Dependence on temperature as

only well as on the amount of impurity

No impurities Trivalent impurity, pentavalent

impurity
P-N JUNCTION:

• When a p-type and n-type semiconductor crystals are combined,

the combination is called a P-N junction.
• It is the building block of all semiconductor devices like diodes,
transistors etc.
• Two important processes occur during the formation of a p-n
junction- diffusion and drift.

There is a difference in the concentration of holes and electrons

at the two sides of a junction. The holes from the p-side diffuse
to the n-side and the electrons from the n-side diffuse to the p-
side. These give rise to a diffusion current across the junction.

• Also, when an electron diffuses from the n-side to the p-side, an

ionised donor is left behind on the n-side, which is immobile. As
the process goes on, a layer of positive charge is developed on
the n-side of the junction. Similarly, when a hole goes from the
p-side to the n-side, an ionized acceptor is left behind on the p-
side, resulting in the formation of a layer of negative charges in
the p-side of the junction. This region of positive charge and
negative charge on either side of the junction is termed as the
depletion region. Due to this positive space charge region on
either side of the junction, an electric field with the direction
from a positive charge towards the negative charge is
developed. Due to this electric field, an electron on the p-side of
the junction moves to the n-side of the junction. This motion is
termed the drift.
 • The direction of the drift current is opposite to that of the
diffusion current.
• When p-type crystal and n-type crystal come in contact, a space
charge region is formed on either side of the p-n junction. This
space charge region is called depletion region.
o The potential difference between the two ends of the
depletion region of a p-n junction is called potential barrier.

SEMICONDUCTOR DIODE OR P-N JUNCTION DIODE:

A p-n junction provided with metallic contacts at the ends for

application of external voltage is called p-n junction diode. P-side is
called anode and n side is called cathode.

Biasing of P-N junction diode:

There are three biasing conditions for the P-N junction diode, and
this is based on the voltage applied:

• Zero bias: No external voltage is applied to the P-N junction

diode.
• Forward bias: The positive terminal of the voltage potential
(battery) is connected to the p-type while the negative terminal
is connected to the n-type.
• The direction of the applied voltage (V) is opposite to the barrier
potential (V0). As a result of this
o In forward bias depletion layer width decreases and
potential barrier height decreases(V0).
o The majority charge carriers, i.e., holes from p side and
electron from n side begin to flow towards the junction.
• I= Ie+Ih

• Reverse bias: The negative terminal of the voltage potential

(battery) is connected to the p-type and the positive is
connected to the n-type.

• The direction of the applied voltage (V) and the barrier potential
(V0) are in the same direction.
 o The majority charge carrier move away from the junction
resulting increase in depletion layer width (W)
o No current flows across the junction due to majority charge
carriers due to increase in barrier width.
However, at room temperature there is always presence of
some minority charge carrier like holes in n-region and
electrons in p-region. The reverse biasing pushes them
towards the junction causing a flow of small current (in
μA). This current is called reverse or leakage current.
The current under reverse bias is voltage independent
upto critical reverse bias voltage known as breakdown
voltage(Vbr ). When V=Vbr , the diode reverse current
increases sharply.
V-I Characteristics of PN Junction Diode
The V-I characteristics of the PN junction diode is a voltage Vs
current graph, that explains the relationship between voltage and
current in a Diode.

In forward bias, I first increases very slowly till the voltage

across the diode crosses a certain value (called Knee voltage or
threshold voltage) and then I increases significantly(exponentially).

Knee voltage for Ge- diode is 0.2 v and for Si- diode is 0.7v.

In reverse bias, I is very small(μA) and remains almost constant with

increase in bias voltage. It is called saturation current. But at a very
high reverse bias voltage called breakdown voltage or Zener voltage
the current increases abruptly.

IDEAL DIODE: Which behaves as a perfect conductor when forward

biased and as a perfect insulator when reverse biased.
PN-JUNCTION AS A RECTIFIER:

➢ A device which converts alternating current (AC) into direct

current (DC) is called rectifier.
➢ PN-junction can be used as both half wave rectifier and full
wave rectifier.
➢ It works on the principle that when a pn-diode is forward biased,
it conduct current and almost negligible current flows through it
when it is reverse biased.

HALF WAVE RECTIFIER:

When the P-N junction diode rectifies half of the ac wave, it is called
half wave rectifier

During positive half cycle of ac the diode is forward biased and

hence DC output current flows across load RL and voltage is
developed across RL.

During negative half cycle of ac the diode is reverse biased and

hence no DC output current flows across load RL and no voltage is
developed across RL.

Thus output voltage is restricted to only in one direction.

Let V = Vm sin t (1) be the applied ac voltage across the
secondary coil.

Vm is the maximum voltage

The instantaneous value of diode current

I = I m sin t for 0  t  
I =0 for   t  2

Vm
Where , Im = maximum amplitude of output current.
rd + R

Here,

rd -internal resistance of diode

R-load resistance
Im
D.C. value of current: I dc =

2
1
I dc =
2  Id (t )
0
 2
1  
=   I m sin t d (t ) +  0. d (t ) 
2  0  
I
= m


Vm
Or I dc =
 (rd + R)
Vm
DC OUTPUT VOLTAGE: Vdc =


The output DC voltage appears at the load resistor R which is

obtained by multiplying output DC CURRENT with the load resistor
R.. The output DC voltage is given as:
Vm
Vdc =

 D.C. power output ( pdc ) rd
EFFICIENCY OF RECTIFIER:  = 100%  = (1 + )  40.53%
Input A.C. power ( pac ) R

Rectifier efficiency is the ratio of output DC power to the input AC

power.

✓ For a half-wave rectifier, rectifier efficiency is 40.6%.

2
Vrms
✓ Ac power input to the load pac = I 2
rms (rd + R) =
rd + R

✓ DC out power across load

2
Vrms
pac = I dc
2
( rd + R ) = ( rd + R )
( rd + R ) 2
2
Vrms
=
( rd + R )
Vm
For half wave rectifier Vrms =
2
2
Vdc
pdc = I dc
2
R=
R

V
2
 Vm 
 
 
2
Vdc 
Therefore,  = R  100% = R  100%
2
Vrms V 
 
( rd + R )  2 
( rd + R)

1
Or  = rd
 40.6%
(1 + )
R
If rd  R then  willbe max imum max  40.6%
RIPPLE FACTOR:   1.21

Ripple factor is the ratio of RMS value of the AC component

(VOLTAGE OR CURRENT) of the output voltage to the DC component
(VOLTAGE OR CURRENT) of the output voltage.
RMS value of the AC component
=
Value of DC component
Vr ( rms )
=
Vdc

After simplification
2
V 
 =  rms  − 1
 Vdc 
2
I 
or  =  rms  − 1
 I dc 

for half wave rectifier

2
 Im
 2
=   − 1 = 1.21
 Im
  

Ripple is the unwanted ac component present in the DC output

which produces pulsation in the rectifier output.

Smaller value of the ac in the dc output, the more effective is the

rectifier.

• Ripple factor can be minimize using capacitor or inductor filter.

PEAK INVERSE VOLTAGE (PIV): Vm is the maximum voltage

It is the maximum reverse voltage that a diode can withstand

without destroying the junction.

FORM FACTOR: 1.57

Form factor (F.F.) is defined as the ratio between RMS load voltage
and average load voltage. The form factor of the half wave rectifier
is as
Vm
Vrms 
F .F. = = 2 =  1.57
Vdc Vm 2


The form factor is used to get the information of the waveform.

Advantages of Half Wave Rectifier

• Affordable
• Simple connections
• Easy to use as the connections are simple
• Number of components used are less

Disadvantages of Half Wave Rectifier

• Ripple production is more

• Harmonics are generated
• Utilization of the transformer is very low
• The efficiency of rectification is low

Applications of Half Wave Rectifier

Following are the uses of half-wave rectification:

• Power rectification: Half wave rectifier is used along with a

transformer for power rectification as powering equipment.
• Signal demodulation: Half wave rectifiers are used for
demodulating the AM signals.
• Signal peak detector: Half wave rectifier is used for detecting
the peak of the incoming waveform.
FULL-WAVE RECTIFIER:

A rectifier which rectifies both halves of ac input is called a full-

wave rectifier.

(a) Centre-taped full wave rectifier

(b) Full wave Bridge rectifier.

Centre-taped full wave rectifier:

During positive half cycle of ac D1 diode is forward biased and D2

diode is reverse biased hence DC output current flows across load RL
for D1 diode while and voltage is developed across RL.

During negative half cycle of ac D2 diode is forward biased and D1

diode is reverse biased hence DC output current flows across load RL
for D2 diode.

Thus, we get pulsating D.C. output voltage.

 2Im Im
D.C. value of current: I dc = I rms =
 2

D.C. power output ( pdc ) rd

EFFICIENCY OF RECTIFIER:  = 100%  = (1 + )  40.53%
Input A.C. power ( pac ) R
2Vm
DC OUTPUT VOLTAGE: Vdc =

Im V
I rms = and Vrms = m
2 2

RIPPLE FACTOR:   .48

2
I 
or  =  rms  − 1
 I dc 

for full wave rectifier

2
 Im 
 
=  2  − 1 = 0.48
 2Im 
  
 

EFFICIENCY OF RECTIFIER:   81.2%

0.812
= 100%
rd
(1 + )
R
If rd  R then  will be max imum, max  81.2%

PEAK INVERSE VOLTAGE (PIV): 2Vm

FORM FACTOR: 1.11

Form factor (F.F.) is defined as the ratio between RMS load voltage
and average load voltage. The form factor of the half wave rectifier
is as
 Vm
Vrms 
F .F. = = 2 =  1.11
Vdc 2Vm 2 2


Full wave Bridge rectifier:

PEAK INVERSE VOLTAGE (PIV): Vm