What is the Hall element?

  Figure 1: Principle of the Hall element

The Hall element is a magnetic sensor that uses the Hall effect. A magnetic field generated by a magnet or an electric current is converted into an electrical signal for output.

The Hall element is an application of the electromagnetic effect on the electric current (known as the "Hall effect"). The Hall effect is named for Dr. E. Hall, a U.S. physicist who discovered this phenomenon in 1879.

Principle of Hall element operation

The Hall element is composed of micrometer order thin film on a semiconductor.
It has electrodes (1), (2), (3) and (4) as shown in Figure 1, and electric current is produced by applying voltage between (1) and (3).
When a magnetic field is applied vertically in the direction that penetrates from the surface of the thin film to the reverse side, the flow of electrons in the semiconductor thin film is bent by Lorentz's force, and the distribution of flow of electrons in the film shifts to the side of the electrode (4).
As a result, potential difference V_Η is generated between the output terminals (2) and (4).
This is called the Hall effect.
The V_Η is called the Hall output voltage and its magnitude can be shown by the following expression.

As shown above, output voltage VH is proportional to the control current IC and magnetic flux density B is obtained by the Hall element.
Where R_Η is a constant called the Hall coefficient, and expressed as follows:

e: Electric charge of electron
n: Carrier density of semiconductor

Drive of the Hall element

There are constant current drive and constant drive modes in the drive mode of the Hall element.

When the Hall element is driven by constant current mode, VH is expressed as follows:

The thermal characteristic of V_Η becomes the characteristic of R_Η, i.e., the thermal characteristic of n.

When the Hall element is driven by constant voltage mode, VH is expressed as follows:

Where, μ_Η is the mobility of the semiconductor and L and W are the width and the length of the semiconductor thin film (See Figure 1).
The thermal characteristic of V_Η becomes the thermal characteristic of μ_Η.

Material of the Hall element

As shown above, output voltage V_Η of the Hall element is dependent on mobility μ_Η and Hall coefficient R_Η of the material.
This means that if the mobility of the material is large, the Hall output voltage is also large.
Accordingly, a III-V family compound semiconductor with large mobility is generally used as the material for the Hall element.

While InSb has the greatest electron mobility among semiconductors, at 78000 (cm²/VS), the temperature dependence is large.
While GaAs has electron mobility of 8500 (cm²/VS), which is about 1/10 that of InSb, the temperature dependence is better with the large band gap.
InAs has intermediate electron mobility and band gap between those of InSb and GaAs, and demonstrates intermediate characteristics between those two semiconductors with high sensitivity and good thermal characteristics.

Offset voltage

Offset voltage Vos is one of the basic characteristics of the Hall element.
Offset voltage is a voltage produced between the output terminals when the magnetic flux density is 0.
This is sometimes called the residual voltage because it is produced only by applying electric current and voltage to the Hall element.
The sum of this offset voltage and the Hall output voltage is produced between the output terminals of the Hall element.
In general, the offset voltage is affected by a variety of factors, such as offset of the pattern when the Hall element is manufactured and lack of uniformity, etc., and it is considerably complex.