# Hall Effect

Hall effect |

### Definition:

The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current.

This hall effect is used to find which type of semiconductor is, and for measuring conductivity and mobility also,

If a specimen(conductor or semiconductor) carrying current I is placed in a transverse magnetic field B, be an electric field E is induced in the direction perpendicular to both I and B.

If I=qnAV

then the force exerted on a carrier due to the magnetic field will be qV*B. This phenomenon is known as Hall effect.

if you see the above figure you will notice that, the current passes through the specimen is in the positive X-direction and B is in the positive Z-direction, A force will be exerted in the negative Y-direction on the current carriers.

so. the current I may be due to holes moving from left to right or due to electrons moving from right to left in the specimen.

so, based on the type of semiconductor the charge carriers accumulated on either side of the specimen. Hence a potential called the Hall voltage appears i.e Vh.Based on the polarity of Vh we can decide what type of semiconductor it is? if it is either n-type or p-type.

Mobility (Î¼) determination :

In the equilibrium state the electric field intensity E due to the hall effect must exert a force on the carrier which just balances the magnetic force,

qE=Bqv

where q-charge,E-electric field, v-drift speed, B-magnetic field Vh-hall voltage.

E=Vh/d

where d-distance between two surfaces of specimen

J=á‹¨v=I/wd

where J-current density, á‹¨-charge density, w-width of the specimen

Vh=Ed=Bvd=BJd/á‹¨=BI/á‹¨w

If Vh,B,I, and w are measured, the charge density can be determined by using above formulae.

Now we are introduced the coefficient is called Hall coefficient as follows,

Rh=1/á‹¨

where Rh is hall coefficient.

Rh=Vhw/BI

The conductivity related to mobility as Ïƒ=á‹¨Î¼

then Î¼=ÏƒRh

This hall effect is used to find which type of semiconductor is, and for measuring conductivity and mobility also,

**Theory:**If a specimen(conductor or semiconductor) carrying current I is placed in a transverse magnetic field B, be an electric field E is induced in the direction perpendicular to both I and B.

If I=qnAV

then the force exerted on a carrier due to the magnetic field will be qV*B. This phenomenon is known as Hall effect.

if you see the above figure you will notice that, the current passes through the specimen is in the positive X-direction and B is in the positive Z-direction, A force will be exerted in the negative Y-direction on the current carriers.

so. the current I may be due to holes moving from left to right or due to electrons moving from right to left in the specimen.

**Hall Effect Operation**so, based on the type of semiconductor the charge carriers accumulated on either side of the specimen. Hence a potential called the Hall voltage appears i.e Vh.Based on the polarity of Vh we can decide what type of semiconductor it is? if it is either n-type or p-type.

Mobility (Î¼) determination :

In the equilibrium state the electric field intensity E due to the hall effect must exert a force on the carrier which just balances the magnetic force,

qE=Bqv

where q-charge,E-electric field, v-drift speed, B-magnetic field Vh-hall voltage.

E=Vh/d

where d-distance between two surfaces of specimen

J=á‹¨v=I/wd

where J-current density, á‹¨-charge density, w-width of the specimen

Vh=Ed=Bvd=BJd/á‹¨=BI/á‹¨w

If Vh,B,I, and w are measured, the charge density can be determined by using above formulae.

Now we are introduced the coefficient is called Hall coefficient as follows,

Rh=1/á‹¨

where Rh is hall coefficient.

Rh=Vhw/BI

The conductivity related to mobility as Ïƒ=á‹¨Î¼

then Î¼=ÏƒRh

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