HALL EFFECT

If a metal or semiconductor carrying current I is placed in a transverse magnetic field B, a

pottential diffrence is produced in the direction normal to both the current and magnetic
field direction. This is called as Hall Effect

It showed that electrons responsible for electrical conduction in metals and there exist
two types of charge carrier in semiconductors

Importance:

1. determines sign of a charge carrier

2. determines charge carrier concerntration
3. determine the mobility of charge carriers, if conductivity of the material is known
4. detrmines the semiconductor is P-Type or N-Type
 Let us consider a rectangular P-type
semiconductor
VH
FI When a pottential diffrence (V) is applied
EH across its ends, current of strength I flows
E through it along X-direction
B

t
Ex If holes are the charge carriers in P-Type
θH semiconductor, then

++++++++++++++++++++ I=pAevd ----[1]

++++++++++++++++++++
p--- concerntration of holes
F A --- Area of cross section of the end face
e--- charge on the hole
Vd --- average drift velocity of holes

V Current Density= Jx=I/A=pevd ----[2]

Any plane perpendiclar to the current flow

direction is an equipottential surface.
Therefore the pottential diffrence between
the front and rare faces F and FI is zero
 ----------------- FI ++++++++++++ FI
P-TYPE N-TYPE
I I
+ FL EH - FL EH

++++++++++++ F ----------------- F

If a magnetic field B is applied normal to the surface and also to the current flow, a
transverse pottential diffrence is produced between F and FI. It is called as Hall Voltage V .
H
after the application of B, the holes experiances a side way deflection due to Lorentz force FL.
The magnitude of the magnetic force is given by

FL=eBvd ---[3]
Because of this force, holes are deflected towards the face F and pile up there and
corresponding equivalent negative charge is left on FI.

As a result an electric field is generated across F and FI.

The direction of the electric field will be from the front to rare face

It is such that it opposes the furthur piling up of holes on front face F.

A condition of equilibrium will be reached when the force FE due to transverse field EH balances
the Lorentz force, FL. The transverse field EH is known as Hall Field.
 Hall field per unit magnetic induction is called as Hall coefficient, RH then

VH= RHBI/t ---[Hall Voltage]

RH= Vht /BI ---[Hall Coefficient]

Hall voltage is areal voltage which can be measured with a voltmeter.

The direction of the B and I, the VH is positive in p type semiconductor but negative in N-
type semiconductor and type of majority charge carriers will be known.

Hall coefficients in metals are independent of temperatures

In case of semiconductor RH, drops sharply with a rise in temperature, indicating that the
concentration of free electrons increases with temperature.
 PN Junction diode

When a crystal of pure semiconductor is doped, so that one half of it is P- type and the other half
is N-Type, then the border between P-Type and N-Type is called P-N Junction

P-Type PN N-Type
The Fermi level in P-Type material is
It has non linear resistance located close to the top of the valance
A junction diode is two terminal device having P-N Junction band, where as in N-Type material
Fermi Level in Unbiased P-N junction diode Fermi level lies close to the bottom of
the conduction band
In P-Type holes and in N-Type free
just at the moment of formation Non-equilibrium condition
electrons are the majority charge
carriers
The closeness of Fermi level to the
valance band on P side indicates that
the lower energy states of the electrons
are empty
the closeness of Fermi level to the
conduction band on N side indicates
that the electrons on N side are in
majority and their overall energy is high
Unbiased diode a few moments after its formation

To reach the equilibrium condition

The electrons diffuses toward P-type from N-Type

The holes diffuses toward N-type from P-
Type
Due to this, difference in charge carrier concerntration in
P and N side of semiconductor. This process is called
diffusion

The diffused charge carriers combine at the junction to

neutralize each other

Due to this neutralisation, a charge free space called

depletion layer is formed near the junction

Due to diffusion of holes from P to N region, negative ions are produced in P-region Similarly Positive
ions in N region
Both these ions are immobile and form barrier across the depletion layer (Charge separation)
Because of this charge separation, an electric pottential or barrier pottential
Barrier is formed then the diffusion of majority charge carrier across the junction is prevented
 PN junction diode under forward bias
P-Side is connected to positive terminal and N side is
connected to negative side of the battery
Due to forward bias equilibrium conditions are disturbed

Therefor energy bands and fermi levels were altered

Due to forward bias energy of an electron in N- side

increases by an amount eV (V- voltage)

Fermi level is raised by eV and the energy bands adjust

their positions so as to suit the elevation of the fermi level

Due to increase in energy in N-side, the pottential barrier is

reduced to e(VB-VF) and the barrier width is reduced

Hence the electrons crossing the junction from N-side will

now face a low potential barier and they can easily cross the
junction

For conduction to take place, forward bias potential

should be greater than the barrier potential
 PN junction diode in reverse bias

N-side is connected to the positive terminal and P

side negative terminal of the battery

This lowers the Fermi level on N-side by an atom

eV raising the barrier height to e(VB+VR) and there
by increasing barrier width

The electrons which are the majority charge

carriers in the N-side will now face a greater
pottential barrier in crossing the junction

The number of electrons crossing from N-Side toP-

side decreases and hence thecurrent is very much
reduced
 NPN Transistor
Majority charge carriers are electrons

A lightly doped and thin P-type semiconductor is sandwich between two N-type semiconductor

Emitter: Source of charge carriers, heavily doped

Base: thin and lightly doped, captures only negligible number of
charge carriers, ie. Controls the flow of charge carriers
Collector: collects the charge carriers, large size

Normally,

E-B junction is always forward biased – low resistance

C-B junction is always Reverse biased – has high resistance
Thus transistor- transfers resistance from low resistance -input
E-B junction to high resistance output

Due to low resistance the voltage across input is low

High resistance the voltage across the output becomes high

Transistor is used as an amplifier

The base is lightly doped, therfor it also amplify current

The battery (VBE) across E-B junction repels the charge carrier in emitter towards base
This constitutes emitter current (IE)

Now the base has opposite polarity,a few charge carriers undergo recombination. These
results in to base current (IB) rest of the charge carriers enter the collector and afterwards they
are attracted towards the battery (VCB)

Thus

IE = IB + IC
Energy Band Diagram of Unbiased NPN transistor
At the instant of its formation (t=0 or non equilibrium)

Pure semiconductor is appropriately doped with suitable

pentavalent and trivalent impurities
Here emitter and Collector are N-Type Due to higher
concerntration of free electrons in conduction band the
fermi levels of these electrodes are near the
conduction band

High concerntration of energetic electrons present in these

electrodes (in CB)

Base is made up of P-Type semiconductor, due to high concerntration of holes, the fermi level of base electrode
is near the valence band
---> absence of energetic free electrons in the conduction band
Presence of Fermi levels at diffrent positions indicates the non equilibrium condition

In the equilibrium condition Fermi levelsin all the regions is equalised EF of E and C
move down and of B should move UP
Few second after its formation

The electrons in the emitter and collector diffuse in the base (near the
junction)
The atoms near the junction from which the elctron leave become positive
ions
The diffusion of electrons from emitter and collector to base and the
diffusion of holes from base to
emitter and collector results in to formation of -VE immobile ions in the
base near the junction

This form barrier at the junction and opposes the further diffusion of
electrons from E andC to base and holes from B to E and C

In energy Band diagram

This indicates as equilibrium situation in which the Fermi levels in all the
regions are equalised resulting in to a single Fermi level of the entire
transistor

The bending of bands results in to the formation of the energy barriers with heights eVEB in emitter- base junction
Electron in the emitter and collector are at lower levels than those in base
Tthey require an energy of about eVBE and eVCB to reach base Fermi level is equalised

An unbiased transistor does not conduct

Biasing NPN transistor
To work as anAmplifier, Transistor should be biased
PN junction is forward biased the energy barrier
decreases (eVBE-eVBE ext)

PN junction is reverse biased the energy barrier

increases(eVCB-eVCBext)
Negative terminal is connected to N-Type,
electrons get energisedand there concerntration
also increases
---> EFE increases by eVBEext
---> pull up energy bands of emitter
--->reduces energy barrier across E-B junction Energy
band and fermi level slightly moves down due to
connection of +VE terminal to B If C-B junction is
reverse biased
---> this depletes the concerntration and energy of
electron in C
--->EFC moves down by eVCBext
---> Energy band pulls down
---> Increases energy barrier acros the C-B
junction

To get Equilibrium, electron must flow from E to B then B to C

i.e. EFE at higher position, EFB at Intermediate position and EFC at lower position
 SOLAR CELL

Diodes which converts light in to electricity are called as solar cells.

The phenomenon of converting the light in to voltage is called as Photovoltaic Effect
Thus solar cells also called as Photovoltaic Cells.
Solar cells are called as Solar Batteries as they give electrical power

solar cell generates the electrical power in four steps

1. Generation of electrons and holes due to light
2. Separation of these electrons and holes due to junction- electric-field
3. Their accumulation across the metal contacts and thus the generation of emf
4. Flow of current due to this emf, when solar cell is connected across a load
When a PN junction is exposed to light,

Photons excite the electrons in the valance band in to conduction band.

These electrons and holes move in opposite direction due to the action of the junction electric field.

Thus all electrons in P region are swept in N region all holes are
swept from N region to P region

The electrons entered in N region continue to flow towards the surface and they accumulate in
the metal contact provided on the surface.

Similarly holes entered in to P region continue to flow towards the surface and accumulate in
the metal contact on the surface.

Thus the N side metal contact acquires negative potential and P side metal contact acquires positive
potential and consequently a potential difference is created across the diode.

If the diode is connected to a load then this PD drives a current in the circuit. Thus we get

electrical power
I-V Characteristics of Solar cell

When the load is not connected (or connected, but very high), the current in the circuit is zero.
Consequently the voltage across the cell is maximum. This is open circuit condition and the
corresponding voltage is called as open circuit voltage (VOC)

The load resistance is reduced to zero, maximum current flows through the circuit, but then the
voltage drops to zero. This is short circuit condition and the corresponding current is called as
short circuit current (ISC)

VOC corresponds to infinite load

ISC corresponds to zero load

Ideal power = PI = ISC × VOC

Workable power = PW = IW × VW
some fraction of ideal power rectangle is ‘filled’ by workable
power rectangle. Greater the ‘filling’, more close is the workable point to the ideal power point. This
can be described by introducing a physical quantity called as fill factor

The optimum load is workable load

Merits:

1. Sunlight is abundantly available and it is inexhaustible.

2. Solar cell does not create any pollution. There is no global warming
3. Solar electricity is risk free electricity. It is safe. There is no fear of accidents.
4. Especially in case of hydraulic power, dams are necessary. This leads to displacement
of people and their rescue. Such problems do not occur in solar electricity.
5. Skilled manpower is not necessary in solar power plant
6. The solar panels can be fitted on houses, street lights or agricultural pumps. This
reduces the transmission losses to a great extent
7. The process of conversion of sunlight in to electricity occurs instantly
8. Low maintenance
Demerits:

1. The sunlight follows day night cycle. The availability of sunlight is also affected due to
change in seasons, change in climate and cloudy weather. Thus solar electricity cannot
be generated continously
2. The electricity generated by solar cells can be stored. But the storage methods are
costly.
3. The efficiency of solar cells is very low (around 10%).
4. Solar electricity is not cheap electricity.
5. Solar electricity is a weak electricity. It is not used when heavy power is required.
6. Solar cells generate DC electricity. In many cases, especially for effective transmission,
AC electricity is required. Therefore conversion of electricity from DC to AC is required.
This requires additional facilities.

Aplications
➢ Supply of electricity in remote areas including villages and deserts, high altitude places
where conventional electricity cannot be transmitted
➢Satellites are the unique application of solar electricity
➢Low power devices such as calculators, toys, LEDs, chargers, Street lights, marine
lights, lights in airports, Solar bicycles, solar cars, solar boats, solar aircrafts etc.
➢Street signals, railway signals etc.
➢Agricultural pumps
▣ Ediswan AR (1922)

▣ Cossor P2 (1922)

▣ Cosmos SP18 (1925)

1
Early Computers Univac
This is the first investigation of a semiconductor.

1833

Resistance (Ohms)
Michael Faraday

Temperature (ºC)

Discovers that electrical resistively decreases as

temperature increases in silver sulfide.
1927 Applied quantum mechanics to solids, helping
explain the conduction of electricity in
semiconductors.

Sommerfeld Bloch
 The Start of the Modern Electronics Era
It can be said that the invention of the transistor and the subsequent development of the microelectronics
have done more to shape the modern era than any other invention.

The first germanium bipolar

Bardeen, Shockley, and Brattain
transistor. Roughly 50 years later,
at Bell Labs - Brattain and
electronics account for 10% (4
Bardeen invented the bipolar
trillion dollars) of the world GDP.
transistor in 1947.
 Electronic Logic

Flip-Flop

A B C S
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0 Half-Adder

Binary Arithmetic S = AxorB (Transistors) (Vacuum Tube)

C = AandB
Transistors didn't need time to "warm up" like the
heaters in vacuum tube circuits.
 Transis
tor

A transistor is a semiconductor device commonly

used to amplify or switch electronic signals.
Integrated Circuits
 Trends in Semiconductors

Smaller Transistors Higher Switching Speeds Declining Costs

The semiconductor industry has been successful in its
consistent efforts to reduce feature size on a chip.
 55,000,000 transistors

105,900,000 transistors

Smaller features mean denser packing of

transistors, which leads to more powerful
computers, more memory, and hopefully lower
costs.
 Stretchable and
Foldable Silicon
Integrated Circuits
 Stretchable and
Foldable Silicon
Integrated Circuits
Germanium Nanoelectronics

Will lead to even smaller, faster transistors!

Polarized LED
Semiconductor Lasers
Quantum Cascade Laser
 THANK YOU
FOR YOUR ATTENTION