Answer to Question #210988 in Electricity and Magnetism for Nabeel khan

Question

Define and explain hall's effect and hall's effect in semi-conductor. Derive the magnitude of hall's voltage. What is the use of hall's effect?

Answer 1

The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current.

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.

When a current-carrying semiconductor is kept in a magnetic field, the charge carriers of the semiconductor experience a force in a direction perpendicular to both the magnetic field and the current. At equilibrium, a voltage appears at the semiconductor edges.

The simple formula for the Hall coefficient given above is usually a good explanation when conduction is dominated by a single charge carrier. However, in semiconductors and many metals the theory is more complex, because in these materials conduction can involve significant, simultaneous contributions from both electrons and holes, which may be present in different concentrations and have different mobilities.

$V_H=\frac{I_xB_z}{nte}.$