Hall effect is defined as the production of a voltage difference across an electrical conductor which is transverse to an electric current, and with respect to an applied magnetic field, it is perpendicular to the current. Edwin Hall discovered this effect in the year 1879.
Hall field is defined as the field developed across the conductor, and Hall voltage is the corresponding potential difference. This principle is observed in the charges involved in the electromagnetic fields.
Consider a metal with one type of charge carrier that is electrons and is a steady-state condition with no movement of charges in the y-axis direction. Following is the derivation of the Hall-effect(at equilibrium, force is downwards due to magnetic field which is equal to upward electric force)
Where,
- VH is Hall voltage
- EH is Hall field
- v is the drift velocity
- d is the width of the metal slab
- B is the magnetic field
- Bev is a force acting on an electron
The ratio between density (x-axis direction) and current density (y-axis direction) is known as the Hall angle, which measures the average number of radians due to collisions of the particles.
Hall Effect Derivation in Semiconductors
In semiconductors, electrons and holes contribute to different concentrations and mobilities, making it difficult to explain the Hall coefficient given above. Therefore, for the simple explanation of a moderateĀ magnetic field
- n is electron concentration
- p is hole concentration
- š¯›¨e is the mobility of electron
- š¯›¨H is the mobility of the hole
- e is an elementary charge
Applications of Hall effect
Hall effect finds many applications.
- It is used to determine if the given material is a semiconductor or insulator.
- It is used to measure the magnetic field and is known as a magnetometer
- They find applications in position sensing as they are immune to water, mud, dust, and dirt.
- They are used in integrated circuits as Hall effect sensors.
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