How to understand Hall Voltage, Hall Electric Field in Hall Effect

The purpose of this lecture is to explain the Hall Electric Field, Hall Voltage in Hall Effect by using the Fleming Left Hand’s Rule which is important point to explain the direction of the magnetic force. The charge carrier hole or electron deviate from the path either upward or downward because of the magnetic force, the direction of force can be explained with the help of Flemming’s left hand rule.

When magnetic force is applied on the charge carrier (here holes) they starts to accumulate on the upper face and as a result downward face becomes negatively charged, where further an Electric field develop in downward direction (from positive face to negative face). As we know that charge is accumulating continuously so at a particular stage the electric field force strength becomes equal to the magnetic field force. In this situation charge particle moves without any deviation further, this is known as steady state.
The two forces are equal and opposite in directions. Now one can define the current which in this case is flowing along the X-axis. By using this current further drift velocity can be derive and can use to derive the result of Hall Voltage.

The Hall Effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879

The Hall Effect is due to the nature of the current in a conductor. Current consists of the movement of many small charge carriers, typically electrons, holes, ions (see Electromigration) or all three. When a magnetic field is present that is not parallel to the direction of motion of moving charges, these charges experience a force, called the Lorentz force. When such a magnetic field is absent, the charges follow approximately straight, ‘line of sight’ paths between collisions with impurities, phonons, etc. However, when a magnetic field with a perpendicular component is applied, their paths between collisions are curved so that moving charges accumulate on one face of the material. This leaves equal and opposite charges exposed on the other face, where there is a scarcity of mobile charges. The result is an asymmetric distribution of charge density across the Hall element that is perpendicular to both the ‘line of sight’ path and the applied magnetic field. The separation of charge establishes an electric field that opposes the migration of further charge, so a steady electrical potential is established for as long as the charge is flowing.

In the classical view, there are only electrons moving in the same average direction both in the case of electron or hole conductivity. This cannot explain the opposite sign of the Hall Effect observed. The difference is that electrons in the upper bound of the valence band have opposite group velocity and wave vector direction when moving, which can be effectively treated as if positively charged particles (holes) moved in the opposite direction to that of the electrons.

Follow the video tutorial below for full information.

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