Hall Effect

When a magnetic field is applied to a current carrying conductor in a direction

perpendicular to that of the flow of current, a potential difference or transverse electric field is
created across a conductor. This phenomenon is known as Hall Effect. This Effect was
discovered by American Physicist Edwin Hall in 1879. The voltage or electric field produced
due to the application of magnetic field is also referred to as Hall voltage or Hall field.

We know that semiconductors are of two types: (i) p-type semiconductor and (ii) n-
type semiconductor.
In the n-type semiconductor, free electrons are the majority carriers and holes are
the minority carriers. That means most of the current in the n-type semiconductor is
conducted by free electrons.
In the p-type semiconductor, holes are the majority carriers and free electrons are
the minority carriers. That means most of the current in the p-type semiconductor is
conducted by holes.

Page 1 of 6
How can we identify whether the semiconductor is p-type or n-type?

Free electrons and holes are the very small particles. So we can’t see them directly
with our eyes. But by using Hall Effect we can easily identify whether the semiconductor is a
p-type or n-type.
When a voltage is applied to a conductor or semiconductor, electric current starts
flowing through it. In conductors, the electric current is conducted by free electrons whereas
in semiconductors, electric current is conducted by both free electrons and holes.
The free electrons in a semiconductor or conductor always try to flow in a straight
path. However, because of the continuous collisions with the atoms, free electrons slightly
change their direction. But if the applied voltage is strong enough, the free electrons
forcefully follow the straight path. This happens only if no other forces are applied to it in
other direction.
If we apply the force in other direction by using the magnetic field, the free electrons in
the conductor or semiconductor change their direction.
Consider a material, either a semiconductor or conductor as shown in the below
figure. When a voltage is applied, electric current starts flowing in the positive x-direction
(from left to right).

If a magnetic field is applied to this current carrying conductor or semiconductor in a

direction perpendicular to that of the flow of current (that is z-direction), an electric field is
produced in it that exerts force in the negative y direction (downwards). This phenomenon is
known as Hall Effect.

Page 2 of 6
Hall Effect in conductor:

The electric field produced in the material pushes the charge carriers downwards. If
the material is a conductor, the electric field pushes the free electrons downwards (that is in
negative y-direction). As a result, a large number of charge carriers (free electrons) are
accumulated at the bottom surface of the conductor.

Because of this large accumulation of negative charges (free electrons) at the bottom
surface and deficiency of negative charges (free electrons) at the upper surface, the bottom
surface is negatively charged and the upper surface is positively charged.

As a result, an electrical difference or potential difference develops between the upper

surface and bottom surface of the conductor. This potential difference is known as Hall
voltage. In a conductor, the electric field is produced due to the negatively charged free
electrons. So the Hall voltage produced in the conductor is negative.

Page 3 of 6
Hall Effect in n-type semiconductor:

If the magnetic field is applied to an n-type semiconductor, both free electrons and
holes are pushed down towards the bottom surface of the n-type semiconductor. Since the
holes are negligible in n-type semiconductor, so free electrons are mostly accumulated at the
bottom surface of the n-type semiconductor.

This produces a negative charge on the bottom surface with an equal amount of
positive charge on the upper surface. So in n-type semiconductor, the bottom surface is
negatively charged and the upper surface is positively charged.

As a result, the potential difference is developed between the upper and bottom
surface of the n-type semiconductor. In the n-type semiconductor, the electric field is
primarily produced due to the negatively charged free electrons. So the Hall voltage
produced in the n-type semiconductor is negative.

Page 4 of 6
Hall Effect in p-type semiconductor:

If the magnetic field is applied to a p-type semiconductor, the majority carriers (holes)
and the minority carriers (free electrons) are pushed down towards the bottom surface of the
p-type semiconductor. In the p-type semiconductor, free electrons are negligible. So holes
are mostly accumulated at the bottom surface of the p-type semiconductor.

So in the p-type semiconductor, the bottom surface is positively charged and the
upper surface is negatively charged.

As a result, the potential difference is developed between the upper and bottom
surface of the p-type semiconductor. In the p-type semiconductor, the electric field is
primarily produced due to the positively charged holes. So the Hall voltage produced in the
p-type semiconductor is positive. This leads to the fact that the produced electric field is
having a direction in the positive y-direction.

Page 5 of 6
How Hall Effect helps to determine the type of a material?

We can easily identify whether a semiconductor is p-type or n-type by using Hall

Effect. If the voltage produced is positive then the material is said to be p-type and if the
voltage produced is negative then the material is said to be n-type.

The Hall voltage is directly proportional to the current flowing through the material, and
the magnetic field strength, and it is inversely proportional to the number of mobile charges in
the material, and the thickness of the material. So in order to produce a large Hall voltage we
need to use a thin material with few mobile charges per unit volume.

Mathematical expression for the Hall voltage is given by:

Where,
VH = Hall voltage
I = current flowing through the material
B = magnetic field strength
q = charge
n = number of mobile charge carriers per unit volume
d = thickness of the material

Applications of Hall Effect:

 Hall Effect is used to find whether a semiconductor is N-type or P-type.

 Hall Effect is used to find carrier concentration.
 Hall Effect is used to calculate the mobility of charge carriers (free electrons and
holes).
 Hall Effect is used to measure conductivity.
 Hall Effect is used to measure a.c. power and the strength of magnetic field.
 Hall Effect is used in an instrument called Hall Effect multiplier which gives the output
proportional to the product of two input signals.

Source: https://www.physics-and-radio-electronics.com/electronic-devices-and-circuits/semiconductor/halleffect.html

Page 6 of 6