HALL EFFECT

HALL EFFECT 

If a metal or a semiconductor carrying a current I is placed in a transverse magnetic field B, a potential difference VH is produced in the direction normal to both the current and magnetic field directions. This phenomenon is called Hall Effect .

Fig: Schematic of Hall Effect Set Up

Applications / importance of Hall Effect 

(i) to determine the type of semiconductor 

(ii) to determine sign of majority charge carriers concentration 

(iii) to determine concentration of majority charge carriers

(iv) to determine mobility of majority charge carriers 

(v) to determine the drift velocity of majority charge carriers.

1) Hall Voltage 

Let us consider a bar of P-type semiconductor crystal and assume the charge carriers to be holes having a charge +e. Let an electric field Ex be applied to the bar which produced a current I in the x-direction in the crystal.

The Current through the semiconductor wafer is given by

Where p is the hole concentration 

             A is the area of cross section of the end face of semiconductor wafer 

             e electrical charge associated with hole 

            vd is the drift velocity of holes

Let a magnetic field B act in the Z-direction. As holes moves in the bar with a velocity, say v, they experience a Lorentz force FL due to the transverse magnetic field B.As a result they deviate sidewise towards the front face of the bar.

        Because of the deflection due to magnetic field, the holes is case of p-type crystal accumulate on front face and make it positively charged while the rare face becomes negatively charged with respect to the front face. Hence a potential VH called the Hall Voltage appears between the front and rare faces.

        The potential builds up in such a way that the electric field EH due to it discourages the further building up of the charges on the faces. The Process of accumulation of charges on front face lasts till the electric field just balances the Lorentz force FL.  
        Once the balance is established the charge accumulation stops and the crystal attains equilibrium states where holes moves parallel to the faces once again.

In the equilibrium state