This phenomenon arises from the Lorentz force: the charge
carriers giving rise to the current flowing through the sample
are deflected in the magnetic field B as a function of their sign
and their velocity v:
(F = force acting on charge carriers, e = elementary charge).
Since negative and positive charge carriers in semiconductors
move in opposite directions, they are deflected in the same
direction.
The type of charge carrier causing the flow of current can
therefore be determined from the polarity of the Hall voltage,
knowing the direction of the current and that of the magnetic
field.