The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductorthat is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879.[1][2]
A Hall effect can also occur across a void or hole in a semiconductor or metal plate, when current is injected via contacts that lie on the boundary or edge of the void or hole, and the charge flows outside the void or hole, in the metal or semiconductor. This Hall effect becomes observable in a perpendicular applied magnetic field across voltage contacts that lie on the boundary of the void on either side of a line connecting the current contacts, it exhibits apparent sign reversal in comparison to the standard ordinary Hall effect in the simply connected specimen, and this Hall effect depends only on the current injected from within the void.[3]
Superposition may also be realized in the Hall effect: Imagine the standard Hall configuration, a simply connected (void-less) thin rectangular homogeneous Hall plate with current and voltage contacts on the (external) boundary which develops a Hall voltage in a perpendicular magnetic field. Now, imagine placing a rectangular void or hole within this standard Hall configuration, with current and voltage contacts, as mentioned above, on the interior boundary or edge of the void. For simplicity, the current contacts on the boundary of the void may be lined up with the current contacts on the exterior boundary in the standard Hall configuration. In such a configuration, two Hall effects may be realized and observed simultaneously in the same doubly connected device: A Hall effect on the external boundary that is proportional to the current injected only via the outer boundary, and an apparently sign reversed Hall effect on the interior boundary that is proportional to the current injected only via the interior boundary. Multiple Hall effects superposition may be realized by placing multiple voids within the Hall element, with current and voltage contacts on the boundary of each void.[3] DE Patent 4308375
The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the charge carriers that constitutes the current.
For clarity, the original effect is sometimes called the ordinary Hall effect to distinguish it from other "Hall effects", which may have additional physical mechanisms, but built on these basics.
https://en.wikipedia.org/wiki/Hall_effect
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