# Hall effect

Hall effect. It is the measurement of the transverse voltage in a conductor when it is placed in a magnetic field . Through this measurement it is possible to determine the type, concentration and mobility of silicon carriers .

A separation of charges appears, giving rise to an electric field inside the conductor perpendicular to the movement of the charges and the applied magnetic field.

## Summary

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• 1 Historical background
• 2 Qualitative explanation
• 3 Quantitative explanation
• 4 Classical physics
• 5 Measurement techniques
• 6 Applying the Hall effect
• 7 Sources

## Historical background

In October 1879 , physicist Edwin Herbert Hall discovered the effect that bears his name. He found that if a high magnetic field is applied to a thin gold foil through which current flows, a voltage is produced across the foil as the current flows, this voltage is called the Hall voltage.

## Qualitative explanation

When an electric current circulates through a conductive or semiconductor material, and this same material is within a magnetic field, it is verified that a magnetic force appears in the charge carriers that regroups them within the material, that is, the carriers Charges deviate and group to one side of the conductive or semiconductor material, thus appearing an electric field perpendicular to the magnetic field and to the electric field itself generated by the battery (Fm).

This electric field is the so-called Hall field (EH), and linked to it appears the Hall voltage, which can be measured using the voltmeter in the figure. In the case of the figure, we have a bar of unknown material and we want to know which are its charge carriers. To do this, using a battery we circulate an electric current through the bar. Once this is done, we introduce the bar into a uniform magnetic field perpendicular to the tablet.

A magnetic force will then appear on the charge carriers, which will tend to group them to one side of the bar, thus appearing a Hall voltage and a Hall electric field between both sides of the bar. Depending on whether the voltmeter reading is positive or negative, and knowing the direction of the magnetic field and the electric field originated by the battery, we can deduce if the charge carriers of the bar of unknown material are the positive or negative charges.

## Quantitative explanation

Let be the material through which the current flows with a speed v to which a magnetic field B is applied. When a magnetic force Fm appears, the charge carriers group together in a region of the material, causing the appearance of a voltage VH and hence an electric field E in the same direction.

This field in turn causes the appearance of an electric force Fe with the same direction but opposite direction to Fm. When these two forces reach a state of equilibrium, the following situation occurs.

## Classical physics

We know that a magnetic field acts on moving charges (Lorentz Force). A current I that passes through a material consists of charges (electrons) that move (in the opposite direction to the current) with a speed that we will call v.

If we immerse that current of electrons in a magnetic field B, each of the electrons that make up the current will be subject to the Lorenz force Fm = -ev ^ B. (as in the drawing the direction of v was changed, since an electron is being considered, the negative sign of the charge should not be considered) Where -e corresponds to the charge of an electron, v the velocity vector of the electron and B the vector applied magnetic field.

The direction of the force will be perpendicular to the plane formed by v and B (since it is the result of the vector product of both) and will cause a displacement of electrons in that direction. As a consequence we will have a concentration of negative charges on one side of the material and a deficit of negative charges on the opposite side.

This distribution of charges generates a potential difference between both sides, the Hall voltage VH, and an electric field EH. This electric field which in turn generates an electric force on the electrons given by Coulomb’s Law, Fe = -e. EH, which acts in the same direction as the Lorentz force but in the opposite direction. The equilibrium will be reached when the sum of the two forces is null, from which we deduce that in the equilibrium the value of the Hall field is: EH = -v ^ B.

## Measurement techniques

Without a doubt, the most widely used measurement technique for determining charge carriers and resistivity in a semiconductor is the Van Der Paw technique. It is also known as a four-pointed technique.

Hall Clamp Model DSC01504 – Hall Effect Meter

The Van Der Pauw technique is used for the determination of resistivity and charge carriers in semiconductors. It is also called a four-pointed technique or a four-corner technique. This technique is generally applied to samples in the form of thin films.

The goal in the Van Der Pauw experiment is to determine the charge carrier density ns by measuring the Hall VH voltage. To measure the Hall voltage VH, a current I is forced to flow through the opposite pair of contacts 1 and 3 and the Hall voltage VH (= V24) is measured in the remaining pair of crossed contacts 2 and 4. On the other hand for resistivity It can be shown that there are two characteristic resistances RA and RB that are related to the resistance of the sheet RS through the equation:

• Exp [- PI (RA / RS)] + Exp [- PI (RB / RS)] = 1

To obtain the two characteristic resistances, a DC current I is applied between contacts 1 and 2 and the voltage V 43 is measured from contact 4 to contact 3. Subsequently, the same current I for contacts 2 and 3, and it is measured the voltage V for contacts 1 and 4.

## Applying the Hall effect

Hall Effect sensors allow to measure:

Hall Sensor – Hall Effect Capture

• The mobility of an electrically charged particle (electrons, gaps, etc.).
• Magnetic fields (Teslameters)
• The intensity of electrical currents (Hall Effect current sensors)
• They also allow the development of non-contact position sensors or detectors, used particularly in the automobile, to detect the position of a rotating shaft (gearbox, driveshafts, etc.).
• Hall effect sensors are also found under the keys of the keyboards of modern music instruments (organs, digital organs, synthesizers) thus avoiding the wear suffered by traditional electrical contacts.
• Hall effect sensors in the encoder of a DC motor.
• Hall Effect (HET) engines are highly efficient plasma accelerators.