The majority carriers in an n-type semiconductor have an average drift velocity V_d in a direction perpendicular to a uniform magnetic field B. The electric field E induced due to Hall Effect acts in the direction

Hall Effect:

When a specimen of metal/semiconductor carrying a current of ‘I’ in the +ve ‘x’ is placed in a magnetic field which is in the positive z-direction, the electric field induces perpendicular to both ‘I’ & ‘V’ in the negative ‘y’-direction.

\(E = \frac{{{V_H}}}{d}\) 

\({V_H} = \frac{{{R_H}BI}}{W}\) 

V_A : Hall voltage

R_H : Hall coefficient

E : Induced Electric field.

Analysis:

The given Semiconductor is of n-type and the average drift velocity of carriers is V_d.

Force is defined as:

F = q E     ---(1)

The force for an n-type semiconductor is:

F = -q (V_d × B) = q (B × V_d)

From Equation (1), the force is induced in the direction of:

\(E = \frac{F}{q} = B \times {V_d}\) 

Note:

Application of Hall-effect:

1) To find the type of semiconductor

2) To find the carrier concentration

3) Mobility can be calculated.