### What is the purpose of Hall Effect?

It is often necessary to
determine whether a material is P-type or n-type. Simply by measuring
conductivity we cannot distinguish between hole and electron conduction.

The Hall Effect can be utilized
to distinguish between two types of carriers, and it also allows the density of
charge carriers to be determined.

### Principle

If
a piece of semi conductor carrying a current is placed in a transverse magnetic
field, an electric field is produced inside the conductor in a direction normal
to both current and magnetic field. This effect is known as Hall Effect and
generated voltage is called Hall Voltage.

Consider an n-type semiconductor slab; the current flow
consists off almost entirely of electrons moving from right to left. This
corresponds to direction of conventional current form left to right.

If ‛V’ is velocity of electrons at right angle to magnetic field,
there is a down ward force on each electron of magnitude Bev. This causes the
electron current to be deflected in a downward direction and causes a negative
charge to accumulate on bottom face of slab. A Potential Difference is established
from top to bottom of specimen with bottom face negative. This Potential Difference
causes Electric field ‛E

_{H}’ in negative ‘Y’ direction and therefore a force ‘eE_{H}’acting in upward direction on electron.
Equilibrium occurs when

eE

_{H}= BeV ------------------- (1)
E

_{H}= Bv -------------------------(2)
If Jx is current density in X – direction then

Jx= neV;

Where

‘V’ is average drift velocity,

‘n’ is concentration of current carriers

The hall effect is described by means off Hall coeff 'RH', defined in terms of current density 'Jx' by relation.

In this case R

_{H}=1/ne; negative sign is used because electric field developed is in negative Y-direction.
All 3 quantities EH, B and JX can be measured and so the hall coeff
and carrier density ‛n’ can be found out.

Determination of Hall Coefficient

The Hall Coefficient is determined by measuring the Hall voltage that
generates the Hall field. If ‛V

_{H}’ is Hall voltage across sample of thickness ‛t’, then
If ‛b’ is width of sample then is cross section will be ‛bt’ and the
current density

Thus,

Note: - the polarity off ‛VH’ will be opposite for ‛n’ type and
‛P’ type semiconductors.

There is another interesting quantity called Hall angle defined by eqn

### Applications of Hall Effect

__Determination of semiconductor Type__

__Calculation of carrier concentration__The hall voltage 'VH' is measured as usual by placing the two probes at centers of top & bottom faces of sample.

**Measurement of magnetic flux density**

Since Hall
voltage is proportional to magnetic flux density ‛B’ for a given current Ix thru a sample, the Hall effect can
be used as basis for the design of a magnetic flux density meter.

**Hall Effect multiplier**
If the magnetic
flux density ‛B’ is produced by passing a current I’ thru an air core coil, ‛B’
will be proportional to I’. The Hall voltage is thus proportional to product of
I & I’. This forms the basis of multiplier.

#### Measurement of Hall Voltage helps in the following

- The sign of current carrying charges can be determined.
- The number of charge carriers present in unit volume can be calculated from magnitude of RH.
- Mobility of charge carriers may be obtained directly from Hall Voltage.