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# Hall effect

The Hall effect refers to the potential difference (Hall voltage) on the opposite sides of an electrical conductor through which an electric current is flowing, created by a magnetic field applied perpendicular to the current. Edwin Hall discovered this effect in 1879.

The ratio of the voltage created to the product of the amount of current and the magnetic field divided by the element thickness is known as the Hall coefficient. It is a characteristic of the material from which the conductor is made, as its value depends on the type, number and properties of the charge carriers that constitute the current.

## Explanation

The Hall effect comes about due to the nature of the current flow in a conductor. Current consists of the movement of many small charge-carrying "particles" (typically, but not always, electrons). These charges experience a force, called the Lorentz Force, when a magnetic field is present that is not parallel to their motion. When such a magnetic field is absent, the charges follow an approximately straight, 'line of sight' path. However, when a perpendicular magnetic field is applied, their path is curved so that moving charges accumulate on one face of the material. This leaves equal and opposite charges exposed on the other face, where there is a dearth of mobile charges. The result is an asymmetric distribution of charge density across the hall element that is perpendicular to both the 'line of sight' path and the applied magnetic field. The separation of charge establishes an electric field that opposes the migration of further charge, so a steady electrical potential builds up for as long as the current is flowing.

For a simple metal where there is only one type of charge carrier (electrons) the Hall voltage VH is given by

$V_H = \frac{-IB/d}{ne}.$

The Hall coefficient is defined as

$R_H=\frac{V_H}{IB/d}=-\frac{1}{ne},$

where I is the current across the plate length, B is the magnetic flux density, d is the depth of the plate, e is the electron charge, and n is the charge carrier density of the carrier electrons.

As a result, the Hall effect is very useful as a means to measure both the carrier density and the magnetic field.

One very important feature of the Hall effect is that it differentiates between positive charges moving in one direction and negative charges moving in the opposite. The Hall effect offered the first real proof that electric currents in metals are carried by moving electrons, not by protons. The Hall effect also showed that in some substances (especially semiconductors), it is more appropriate to think of the current as positive "holes" moving rather than negative electrons.

### Hall effect in Semiconductors

When a current carrying semiconductor is kept in a magnetic field, the carriers of the semiconductor experience a force in a direction perpendicular to the magnetic field and current field, this is called Hall effect in semiconductors.

$V=\frac{Eh}{B}$

Eh = Hall field

The simple formula for the Hall coefficient given above becomes more complex in semiconductors where the carriers are generally both electrons and holes which may be present in different concentrations and have different mobilities. For moderate magnetic fields the Hall coefficient is

$R_H=\frac{-n\mu_e^2+p\mu_h^2}{e(n\mu_e+p\mu_h)^2}$

where $\, n$ is the electron concentration, $\, p$ the hole concentration, $\, \mu_e$ the electron mobility , $\, \mu_h$ the hole mobility and $\, e$ the electronic charge.

For large applied fields the simpler expression analogous to that for a single carrier type holds.

$R_H=\frac{1}{(n-p)e}$

### Technological applications

So-called "Hall effect sensors" are readily available from a number of different manufacturers, and may be used in various sensors such as fluid flow sensors, power sensors, and pressure sensors. Also many other applications in some electric airsoft guns and often used on the triggers of many electropnuematic paintball guns.

### Quantum Hall effect

For a two dimensional electron system which can be produced in a mosfet transistor. In the presence of large magnetic field strength and low temperature, one can observe the quantum Hall effect, which is the quantization of the Hall voltage.

### Quantum Spin Hall Effect

For HgTe two dimensional quantum wells with strong spin-orbit coupling, in zero magnetic field, at low temperature, the Quantum Spin Hall Effect has been recently observed.

### Hall effect in magnetic systems

In ferromagnetic materials (and paramagnetic materials in a magnetic field), the Hall resistivity includes an additional contribution, known as the Anomalous Hall Effect (or the Extraordinary Hall effect), which depends directly on the magnetization of the material, and is often much larger than the ordinary Hall effect. (Note that this effect is not due to the contribution of the magnetization to the total magnetic field.) Although a well-recognized phenomenon, there is still debate about its origins in the various materials. The anomalous Hall effect can be either an extrinsic (disorder-related) effect due to spin-dependent scattering of the charge carriers, or an intrinsic effect which can be described in terms of the Berry phase effect in the crystal momentum space (k-space).

## Applications

Hall effect devices produce a very low signal level and thus require amplification. While suitable for laboratory instruments, the vacuum tube amplifiers available in the first half of the 20th century were too expensive, power consuming, and unreliable for everyday applications. It was only with the development of the low cost integrated circuit that the Hall effect sensor became suitable for mass application. Many devices now sold as "Hall effect sensors" are in fact a device containing both the sensor described above and a high gain integrated circuit (IC) amplifier in a single package. Recent advances have resulted in the addition of ADC (Analog to Digital) converters and I²C (Inter-integrated circuit communication protocol) IC for direct connection to a microcontroller's I/O port being integrated into a single package, see Advanced Hall Effect Current Transducer. Reed switch electrical motors using the hall effect IC is another application.

Hall probes are often used to measure magnetic fields, or inspect materials (such as tubing or pipelines) using the principles of Magnetic flux leakage.

Hall effect devices when appropriately packaged are immune to dust, dirt, mud, and water. These characteristics make Hall effect devices better for position sensing than alternative means such as optical and electromechanical sensing.   When electrons flow through a conductor, a magnetic field is produced. Thus, it is possible to create a non-contacting current sensor. The device has three terminals. A sensor voltage is applied across two terminals and the third provides a voltage proportional to the current being sensed. This has several advantages; no additional resistance (a shunt, required for the most common current sensing method) need be inserted in the primary circuit. Also, the voltage present on the line to be sensed is not transmitted to the sensor, which enhances the safety of measuring equipment.

#### Ferrite toroid Hall effect current transducer

Hall sensors can detect stray magnetic fields easily, including that of Earth, so they work well as electronic compasses: but this also means that such stray fields can hinder accurate measurements of small magnetic fields. To solve this problem, Hall sensors are often integrated with magnetic shielding of some kind. For example, a Hall sensor integrated into a ferrite ring (as shown) can reduce stray fields by a factor of 100 or better. This configuration also provides an improvement in signal-to-noise ratio and drift effects of over 20 times that of a 'bare' Hall device. The range of a given feedthrough sensor may be extended upward and downward by appropriate wiring. To extend the range to lower currents, multiple turns of the current-carrying wire may be made through the opening. To extend the range to higher currents, a current divider may be used. The divider splits the current across two wires of differing widths and the thinner wire, carrying a smaller proportion of the total current, passes through the sensor.

The principle of increasing the number of 'turns' a conductor takes around the ferrite core is well understood, each turn having the effect of 'amplifying' the current under measurement. Often these additional turns are carried out by a staple on the PCB.

#### Split ring clamp-on sensor

A variation on the ring sensor uses a split sensor which is clamped onto the line enabling the device to be used in temporary test equipment. If used in a permanent installation, a split sensor allows the electrical current to be tested without dismantling the existing circuit.

### Analogue multiplication

The output is proportional to both the applied magnetic field and the applied sensor voltage. If the magnetic field is applied by a solenoid, the sensor output is proportional to product of the current through the solenoid and the sensor voltage. As most applications requiring computation are now performed by small (even tiny) digital computers, the remaining useful application is in power sensing, which combines current sensing with voltage sensing in a single Hall effect device.

### Power sensing

By sensing the current provided to a load and using the device's applied voltage as a sensor voltage it is possible to determine the power dissipated by a device. This power is (for direct current devices) the product of the current and the voltage. With appropriate refinement the devices may be applied to alternating current applications where they are capable of reading the true power produced or consumed by a device.

### Position and motion sensing

Hall effect devices used in motion sensing and motion limit switches can offer enhanced reliability in extreme environments. As there are no moving parts involved within the sensor or magnet, typical life expectancy is improved compared to traditional electromechanical switches. Additionally, the sensor and magnet may be encapsulated in an appropriate protective material.

#### Automotive ignition and fuel injection

If the magnetic field is provided by a rotating magnet resembling a toothed gear, an output pulse will be generated each time a tooth passes the sensor. This is used in modern automotive primary distributor ignition systems, replacing the earlier contact breaker ('points', which were prone to wear and required periodic adjustment and replacement). Similar sensor signals are used to control multi-port sequential fuel injection systems, where each cylinder's intake runner is fed fuel from an injector consisting of a spray valve regulated by a solenoid. The sequences are timed to match the intake valve openings and the duration of each sequence by the Engine Control Unit (computer).

#### Wheel rotation sensing

The sensing of wheel rotation is especially useful in anti-lock brake systems. The principles of such systems have been extended and refined to offer more than anti-skid functions, now providing extended vehicle "handling" enhancements.

#### Solar Car energy management

Accurate and efficient management of all aspects of energy is a critical aspect of any successful solar car - Hall effect current transducers are an ideal solution due to their high accuracy, environmental hardiness and low power consumption.

#### Electric motor control

Some types of brushless DC electric motors use Hall effect sensors to detect the position of the rotor and feed that information to the motor controller.

#### Industrial Applications

Applications for Hall Effect sensing have also expanded to the industrial/off-highway market, which now use Hall Effect Joysticks to control hydraulic valves, replacing the traditional mechanical levers. Such applications include; Mining Trucks, Backhoe Loaders, Cranes, Diggers, Scissor Lifts, etc. A leading manufacturer of Industrial Hall Effect Joysticks is P-Q Controls, Inc., which was one of the first companies to expand the use of Hall Effect sensing to such applications in the 1980's, and in fact holds exclusive patents for contactless sensing.

## The Corbino effect

The Corbino effect is a phenomenon similar to the Hall effect, but a disk-shaped metal sample is used in place of a rectangular one. A radial current through a circular disc subjected to a magnetic field perpendicular to the plane of the disk, produces a "circular" current through the disk.