Hall Effect Applications of Hall Effect

The Hall effect is the sideways shift of carriers when a current carrying conductor inside a magnetic field sits in a field at right angles to the current. The Lorentz force on those carriers depends on the magnetic field and on the current direction. electric current is a flow of charge: electrons in a metal, electrons and holes in a semiconductor. Holes follow conventional current. Electrons go the other way. Each charged carrier feels a force in that conductor, piles up on one face, and a small voltage appears across the sample. That voltage is the Hall voltage.

The metal block below is drawn as if it were transparent.

A voltage drives current I from left to right (x). Flux density B points along y. Fleming’s left-hand rule then gives a force from that current and that magnetic field. Conduction electrons are driven toward the bottom face, so the top and bottom differ in electron density. A small voltage appears along z. The electric field of that charge pile-up pushes back on later electrons. Two forces then act on each carrier.

1. The force due to Hall effect
2. The force due to created electric field

The force due to the Hall effect and the force due to the created electric field are opposite to each other. When a certain electric field is established due to the Hall effect, the system reaches equilibrium. At this point, the forces on the charge carriers (electrons) from the electric field and the Hall effect are equal and opposite. This balance prevents further shifting of electrons, maintaining the system in equilibrium.
Let us concentrate on a single charge carrier moving through a conductor placed inside a magnetic field.
The charge of the charge carrier is e (say)
The magnetic flux density of the field is B (say).
Now we can write the magnetic force acting on the current carrying conductor of active length L and current I as

When the direction of B and I are perpendicular to each other.

We can rewrite the above equation as

Where V is the velocity of the charge passing through the conductor.

From the above equation, we can write the force acting on a single charge carrier as,

Where v is the drift velocity of the charge carriers.
Now we can write the field created due to Hall effect as, E_H.
Hence, we can write the force acting on the charge carrier due to the field as

Now at equilibrium

Now we consider N is charge carrier concentration.

From equation 1 and 2, we can write

We call the term as the Coefficient of Hall Effect or simply Hall Coefficient. We define Hall Coefficient as the Hall field per unit magnetic field density per unit current density.

Application of Hall Effect

The Hall effect is used to
Determine the Type of Semiconductor
Hall-voltage polarity shows whether the sample is an n-type semiconductor or a p-type semiconductor. The Hall coefficient is negative in n-type material and positive in p-type material.

Calculate the Carrier Concentration
The expressions for the carrier concentrations of electrons (n) and holes (p) in terms of Hall coefficient are given by

Determine the Mobility (Hall Mobility)
Mobility expression for the electrons (μ_n) and the holes (μ_p), expressed in terms of Hall coefficient is given by,

Where, σ_n and σ_p represent the conductivity due to the electrons and the holes, respectively.

Measure Magnetic Flux Density
This equation can be readily deduced from the equation of Hall voltage and is given by

Further, there are many commercially available types of equipment based on the principle of Hall effect including Hall-effect sensors and Hall-effect probes.