Device to Find Hall Effect [Experiment]

DEVICE TO FIND HALL EFFECT [EXPERIMENT]

Experimental set up

A semiconductor slab of thickness 't' and breadth 'b' is taken and current is passed using the battery as shown in Fig. 2.30.

The slab this placed between the pole pieces of an electromagnet so that current direction coincides with x-axis and magnetic field coincides with z-axis. The Hall voltage (V_H) is measured by placing two probes at the center of the top and bottom faces of the slab (y-axis).

If B is magnetic field applied and the V is the Hall voltage produced, then the Hall coefficient can be calculated from the formula

Mobility of Charge Carriers

In general the Hall Co-efficient can be written as 

The above expression is valid only for conductors where the velocity is taken as the drift velocity.

But for semiconductors velocity is taken as average velocity so R_H for an 'n' type semiconductor is modified as

………(1)

We know the conductivity for n type is σ_e =n_e eμ_e

(or)  ……….(2)

From equation (1) we can write

 ………(3)

Substituting equation (3) in equation (2) we get

The mobility of electron is in an n-type semiconductor is

Similarly for p-type Semiconductor, the mobility of hole is

Thus by finding Hall voltage, Hall coefficient can be calculated and thus the mobility of the charge carriers (μ_e and μ_h) can also be determined.

Hall Angle (Ɵ_H)

We know if the current (E_x) is applied to a specimen along x direction, magnetic field (B) along z-direction then Hall voltage (E_H) is produced along y-direction (Fig 2.31).

Here the Hall angle can be measured from the formula

 …….(1)

we know, Е_H = R_HJ_X B ………(2)

We know E_H=V_x B ……..(3)

Substituting equation (3) in equation (1) we get

(or) 

Where μ = V_x/E_x

Thus the mobility (μ) can be defined as the velocity acquired by the charge carrier per unit electric field.