Imagine a wide piece of wire with current flowing through it. Put it in a magnetic field and the electrons feel a force:

F_B = force on electron due to magnetic field.

Stronger magnetic field → larger force down.

So electrons build up on the bottom edge of the wire making it more negative.

However, this makes it less attractive to the next electrons, who find themselves pushed down by the magnetic field but repelled up by the build up of electrons.

F_E = force up on electrons due to repulsion by other electrons.

Eventually the two forces balance and all further electrons entering the wire travel through it in a straight line. This is called the Hall Effect.

At this point you can measure the pd between the top and bottom of the wire. This pd is called the Hall voltage. It depends on the strength of the magnetic field so it can be used to measure magnetic field strength.

Where:

B = magnetic field strength (T)

V = drift velocity of electrons (ms^-1)

d = width of the conductor (m)

Obviously, the Hall Effect gives a larger voltage if the conductor is wide (d large) and if V is large. In metals, the current consists of large numbers of electrons moving slowly but in semiconductors, there are fewer charge carriers moving much quicker. For this reason, Hall probes are usually made with a wide, flat piece of semiconductor.