Hall Effect

Principle

When a current carrying semiconductor is placed in a transverse magnetic field, a voltage is induced in the semiconductor direction perpendicular to both the current and magnetic field. This phenomenon is called Hall effect. The induced voltage is called Hall voltage (V_H). It was discovered by Hall in 1879.

Figure 1. Schematic diagram of the Hall effect experiment.

Theory

Consider a rectangular slab of an n-type semiconductor material of width (w), thickness (t) and that carries a current I along the positive X-direction and magnetic field B be applied along the positive Z-direction. Under the influence of this magnetic field, the electron experience a force called Lorentz force given by

This Lorentz force is exerted on the electrons in the negative Y-direction. The direction of this force is given by Fleming’s left-hand rule. Thus, the electrons are, therefore, deflected downwards and collect at the bottom surface of the specimen.

On the other hand, the top edge of the specimen becomes positively charged due to the loss of electrons. Hence, a potential called the Hall voltage V_H is developed between the upper and lower surfaces of the specimen, which establishes an electric field E called the Hallfield across the specimen in the negative Y-direction

The force acts on the charges in the presence of magnetic field can be written as

The force acts on the charges in the presence of generated electric field,

Under the equilibrium condition, the force due to electric component will counter balance that of magnetic force.

The current density the semiconductor will be,

Substitute v_d value in Eqn 8,

Where R_H = −1/ne is the Hall co-efficient.

We can write R_H as

where E_H =V_H/t

We know current density Jx = I/A =I/(w×t). Hence R_H will be

If R_H is positive, it is a p-type semiconductor. If R_H is negative, it is a n-type semiconductor

Applications of Hall effect

1. To asses the type of semiconductor, whether it is a p-type or n-type.
2. The evaluation of concentration of charge carriers.
3. The calculation of mobility of charge carriers.
   
4. To measure the strength and direction of magnetic field.