Hall effect in p-type semiconductor

Hall effect in p-type semiconductor

Similar to n-type semiconductor, we can write for p-type semiconductor

where p is concentration of holes.

The positive sign indicates that the electrical field (Hall field) is developed in positive Y- direction.

Hall coefficient in terms of Hall voltage

If t is the thickness of the sample and VH is the voltage  developed, then

If b is breadth of the sample, then

Cross sectional area of the sample (A) = Breadth (b) x Thickness (t) = bt

Determination of Hall coefficient

The experimental arrangement to measure Hall-coefficient is shown in fig. 3.18.

A semiconductor is taken in the form of a rectangular slab of thickness t and breadth b. A suitable current Ix ampere is passed into this sample along X-axis by connecting it to a battery.

Now, it is placed in between north and south poles of an electromagnet. The magnetic field is applied along Z-axis.

Due to Hall effect, Hall voltage (VH) is developed in the sample. This voltage is measured by fixing two probes at the centers of the bottom and top faces of the sample.

By measuring Hall voltage, Hall coefficient is determined from the formula

 From Hall coefficient, carrier concentration and mobility can be determined.

Applications of Hall effect

(i) Determination of semiconductor type

The sign of the Hall coefficient is used to find whether a given semiconductor is n-type or p-type.

(ii) Calculation of carrier concentration

By measuring Hall coefficient RH, carrier concentration is determined from the relation.

(iii) Determination of mobility

We know that electrical conductivity,