If we place a current carrying conductor or semiconductor in a perpendicular magnetic field B (fig. 1) then an electric field arises perpendicular to the I-B surface. This effect is known as the Hall-effect. This effect was discovered in 1879 by the American physicist Edwin Herbert Hall.
Figure 1. Hall effect
Consider a current composed of holes (I ) flowing in the positive x-direction. Due to the magnetic field the holes are forced towards the lower surface (2). Side 2 of the conductor is positive relative to surface 1, in other words an electric field E exists in the positive y-direction, and therefore perpendicular to the x-z surface (I-B surface).
A Hall voltage is generated, , between the electrodes 1 and 2.
In equilibrium the electric field will exercise a force (with opposite polarity) equal to the force of the magnetic field on the flowing charge carriers:
with q = charge and v = drift velocity. From this it follows:
If there are n holes per m3 then the charge density is:
If this charge is displaced with a drift velocity v (m/s) then the current density is:
The current density may also be written as: , so that:
With the Hall constant of the material, , this becomes:
Table 1. Hall constants
In contrast to metals some semiconductors (e.g. indium based) have an important RH value (see table 1).
From the possible applications follow.
- With a constant current a magnetic field can be measured:
- With constant magnetic field, e.g. from a permanent magnet, it is possible to measure currents:
- If I is made proportional to the first input signal (V1) and B is proportional to a second input signal (V2), then and we have a Hall-effect multiplier. In this way we can measure power:
A thin layer of a few μm of semiconductor material placed on a ceramic substrate is sufficient to make a sensor for detecting magnetic fields.
The semiconductor can be InSb (= indiumantimonide). A constant current is caused to flow through the semiconductor. If a perpendicular magnetic field is present at the sensor, then there is an output voltage (VH).
In practical sensors this voltage is 0.2 to 1V/T , hereby: 1 T ( Tesla ) = 1Wb/m2.
A differential amplifier is usually integrated into the sensor to produce a useful output voltage.