Hall Effect describes the behavior of free charge carriers in the semiconductor when subjected to the electric and magnetic fields. The phenomenon was discovered by Edwin Hall in 1879 and can be considered as an extension of Lorentz force, which describes the force exerted on a charged particle moving through a magnetic field.

It is well known that a potential applied across the semiconductor material causes the electrons within it to move in the direction opposite to that of the applied field. (figure a)

Further, it is to be noted that, in this case, the path of the electrons will be almost a straight line. Now if the same material is subjected to the transverse magnetic field, the electrons start moving along the curved path as shown by Figure b due to the force exerted by the applied magnetic field on them.

This leads to the increase in the number of electrons on one side of the semiconductor while the corresponding opposite side experiences electron deficiency.

As a result, there is a voltage developed across these two sides of the semiconductor material as show by pink lines in the Figure b. The voltage so developed is called Hall Voltage $(V_H)$ and the associated phenomenon is referred to as Hall Effect.

Moreover, the direction of the Hall voltage so developed will be perpendicular to both the direction of current flow as well as to the applied magnetic field.

Thus, the Hall Effect can be stated as the phenomenon where the current carrying conductor or semiconductor subjected to the external magnetic field develops a voltage across its terminals in the direction perpendicular to both the flow of current as well as to the direction of applied magnetic field.

Mathematical expression for the Hall voltage is given by

$V_H=\frac{IB}{qnd}$

Where,

I represents current flowing through the sample

B represents the strength of the magnetic field

q represents the charge

n is the number of mobile charge carriers per unit volume

d represents the thickness of the sample

Here the term 1/(qn) is called the Hall Coefficient (RH) and is negative if the majority charge carriers are electrons while positive if the majority charge carriers are holes.