Hall probes have accomplished a rapidly growing demand in the past years, although, the Hall effect was discovered by Edwin H. Hall in 1879. 

Figure 1 shows principle of the Hall effect:

 

General 1

Figure 1

 

Four leads are connected to the midpoints of opposite sides of semiconductor layer (e.g. InSb, InAs). When current I [A] is fed trough the semiconductor plate and magnetic field with induction B [T] is applied, then current density is defined

General 2

 

where n [m-3] is the charge carrier density and e [C] is the electronic charge, v [ms-1] is electron drift velocity and ab [m2] is cross-section of the plate. The current density has direction of positive axes Y but the charge carriers are moving in direction -Y. Velocity v of the charge carriers is proportional to the current.

General 3

 

To the electron will affect force F [N] along axis Y of the electric field of the power source ξ, and magnetic force in positive direction of the axis X, which will move the electron to the frontal side of the plate.

General 4

 

Electron density in the equilibrium state will be higher near the frontal side of the plate and the electron deficiency (the positive charge) will be near the rear side. In consequence of this charge distribution the electric field intensity EH [Vm-1] of the plate will increase in the direction of the axis X which is equal to vB.

General 5

 

The field EH is a Hall field which compensates influence of magnetic force F on electrons. The Hall voltage UH [V] will be observed between the frontal and rear side of the plate with width b [m]:

General 6

 

The resultant magnitude of the differential Hall voltage UH of the circuit can be measured by a voltmeter. The RH [m3C-1] is a Hall coefficient which depends on the character of the material forming the active area of the probe. The magnitude of the Hall coefficient is given by the equation:

General 7

 

Hall probe is a device that utilizes the Hall effect for the purpose of generating a direct output voltage in the presence of a magnetic field. If constant control current IC fed the Hall probe at a given sensitivity KH [VA-1T-1] a Hall voltage UH is directly proportional to the magnetic flux density B. The voltage output varies with the angle θ (in degrees) between the vector of the magnetic flux lines and the plane of the sensing area. The maximum value is reached when the magnetic flux lines are perpendicular to the sensing area.

General 8

 

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