Hall effect - Principle, Theory, Applications and Limitations

Hall Effect 

It is the generation of potential difference across electrical conductors, traversed to electric current in the conductor and to the magnetic field perpendicular to current. The voltage produced is called Hall voltage.

Theory 

The Hall effect was given by E. H. Hall in 1879. He measured the traversed electric field, when a current carrying conductor is placed in a magnetic field which is perpendicular to the electric current. When a charged particle is placed in the magnetic field, it experiences a force which is known as lorentz force which drifts the charge particle in a particular direction. The concentration of these charge particles in that direction increases which induces a potential difference which is known as Hall voltage. 

The number of charge particles, type of charge carrier and mobility cannot be measured properly with the help of electrical conductivity. So the hall effect is used to find such parameters. 

Hall effect also helps to differentiate the type of charge carrier (electrons and holes) with the help of the hall coefficient.

Measurement of Hall mobility and Carrier concentration 

Consider a n-type semiconductor with a rectangular cross-section as shown in fig. Let current is flowing along the x-axis and magnetic field (B) applied along the z-axis and electrons are flowing from right to left. 

Let v = velocity of electron perpendicular to B

Force on electron = Bev (downward) 

Electrons will be collected at bottom 

V = Potential difference produced 

let E = Electric field produced from top to bottom 

Force due to potential difference for electric field = e E (upward)

In equilibrium eE = eBv

E = Bv  ....(1)

The electric current I is given by 

I = neAv = netbv  ....(2) 

where t is the thickness and b is the breadth of the rectangular slab. 

v = I/netb 

put this value in equation (1)

E = IB/netb = RH IB/tb   ....(3)

where RH = 1/ne is called Hall coefficient 

Since E = V/b  ....(4)

from equation (3) and (4), we get 

V = Ib/tne

so, RH = 1/ne = Vt/IB

In this case RH = -1/ne = Vt/IB

A negative sign shows that an electric field is produced along the y-axis. 

Similarly for p-type semiconductor 

RH = 1/pe = Vt/IB 

From Hall coefficient, we get 

(a) carrier mobility - 

we know that the conductivity of n-type semiconductors is given by 

σ = -neμ

μ = -σ/ne = -σRH

Here the values of V, t, I and B can be measured directly and conductivity or either unknown value can be measured. 

(b) Determination of Carrier concentration - 

So,  RH = 1/ne

n = 1/eRH = IB/eVt

Applications of Hall effect - 

• To determine the type of semiconductor with the help of sign on hall coefficient.
• To determine carrier concentration.
• To determine mobility.
• Sensors - This effect is used in magnetic field sensing devices, current sensing devices, speed sensing devices etc. 
• Used in magnetic levitation trains 
• Used in position sensing devices like joystick controllers, robotics etc. 
• For the measurement of current. 

Frequently Asked Questions - FAQs

Q1. which force is responsible for the hall effect ?

Lorentz force

Q2. what is lorentz force ?

Lorentz force - Force experienced by a charge particle when it placed in electric and magnetic field. 

Q3. what are the limitations of the hall effect ?

Hall effect is temperature dependent 

The hall effect only works in the case of a perpendicular magnetic field. 

Affected by external factors. 

Q4. Why is the hall effect not observed in metals ?

As we discussed above the hall voltage is inversely proportional to the charge carrier density, so metal has a high number of charge carriers. so the hall effect is not observed in metals.

Q5. Why is semiconductor used in the hall effect ?

In the case of semiconductors the charge density is less so the hall effect is more effective in case of semiconductors.

Q6. What is the principle of hall effect ?

When a current carrying semiconductor is placed inside a perpendicular magnetic field, a voltage is generated which is perpendicular to the direction of current.

Q7. Can the hall coeffiecient be zero ?

Yes, in the case of an insulator, its value is almost zero.

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