Hall Effect
Hall Effect
Hall Effect
Hall effect
The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse
to an electric current in the conductor and a magnetic field perpendicular to the current. It was discovered by Edwin
Hall in 1879.[1]
The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the
applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends
on the type, number, and properties of the charge carriers that constitute the current.
Discovery
The Hall effect was discovered in 1879 by Edwin Herbert Hall while he was working on his doctoral degree at Johns
Hopkins University in Baltimore, Maryland. His measurements of the tiny effect produced in the apparatus he used
was an experimental tour de force, accomplished 18 years before the electron was discovered.
Theory
The Hall effect comes about due to the nature of the current in a conductor. Current consists of the movement of
many small charge carriers, typically electrons, holes, ions (see Electromigration) or all three. Moving charges
experience a force, called the Lorentz force, when a magnetic field is present that is perpendicular to their motion.[2]
When such a magnetic field is absent, the charges follow approximately straight, 'line of sight' paths between
collisions with impurities, phonons, etc. However, when a perpendicular magnetic field is applied, their paths
between collisions are 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 scarcity 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 charge is flowing.
It shall be noted that in the classical view, there are only electrons moving in the same average direction both in the
case of electron or hole conductivity. This cannot explain the opposite sign of the Hall effect observed. The
difference is that electrons in the upper bound of the valence band have opposite group velocity and wave vector
direction when moving, which can be effectively treated as if positively charged particles (holes) moved in opposite
direction than the electrons do.
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For a simple metal where there is only one type of charge carrier (electrons)
the Hall voltage VH is given by
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.
The Hall coefficient is defined as
where j is the current density of the carrier electrons, and is the induced electric field. In SI units, this becomes
As a result, the Hall effect is very useful as a means to measure either the carrier density or 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 p-type semiconductors), it is more appropriate to think of the current as positive "holes"
moving rather than negative electrons. A common source of confusion with the Hall Effect is that holes moving to
the left are really electrons moving to the right, so one expects the same sign of the Hall coefficient for both
electrons and holes. This confusion, however, can only be resolved by modern quantum mechanical theory of
transport in solids.[3]
It must be noted though that the sample inhomogeneity might result in spurious sign of the Hall effect, even in ideal
van der Pauw configuration of electrodes. For example, positive Hall effect was observed in evidently n-type
semiconductors.[4]
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where is the electron concentration, the hole concentration, the electron mobility , the hole mobility
and the absolute value of the electronic charge.
For large applied fields the simpler expression analogous to that for a single carrier type holds.
with
where
e is the elementary charge (approx. 1.6 × 10-19 C)
B is the magnetic field (in teslas)
me is the electron mass (approx. 9.1×10-31 kg).
The Hall parameter value increases with the magnetic field strength.
Physically, the trajectories of electrons are curved by the Lorentz force. Nevertheless when the Hall parameter is
low, their motion between two encounters with heavy particles (neutral or ion) is almost linear. But if the Hall
parameter is high, the electron movements are highly curved. The current density vector, J, is no more colinear with
the electric field vector, E. The two vectors J and E make the Hall angle, θ, which also gives the Hall parameter:
When a current carrying metallic wire is placed in an external magnetic field in direction perpendicular to the
direction of flow of current, an electric field is produced in the wire in direction perpendicular to both the direction
of current and direction of magnetic field.
Applications
Hall probes are often used as magnetometers, i.e. to measure magnetic fields, or inspect materials (such as tubing or
pipelines) using the principles of magnetic flux leakage.
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
in fact contain both the sensor as described above plus a high gain integrated circuit (IC) amplifier in a single
package. Recent advances have further added into one package an analog-to-digital converter and I²C
(Inter-integrated circuit communication protocol) IC for direct connection to a microcontroller's I/O port.
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Contemporary applications
Hall effect sensors are readily available from a number of different manufacturers, and may be used in various
sensors such as rotating speed sensors (bicycle wheels, gear-teeth, automotive speedometers, electronic ignition
systems), fluid flow sensors, current sensors, and pressure sensors. Common applications are often found where a
robust and contactless switch or potentiometer is required. These include: electric airsoft guns, triggers of
electropneumatic paintball guns, go-cart speed controls, smart phones, and some global positioning systems.
The principle of increasing the number of windings a conductor takes around the ferrite core is well understood, each
turn having the effect of multiplying the current under measurement. Often these additional turns are carried out by a
staple on the PCB.
Analog 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 the 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.
Current 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.
Industrial applications
Applications for Hall Effect sensing have also expanded to industrial applications, 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.
Spacecraft propulsion
A Hall effect thruster (HET) is a relatively low power device that is used to propel some spacecraft, once they get
into orbit or farther out into space. In the HET, atoms are ionized and accelerated by an electric field. A radial
magnetic field established by magnets on the thruster is used to trap electrons which then orbit and create an electric
field due to the Hall effect. A large potential is established between the end of the thruster where neutral propellant is
fed and the part where electrons are produced, so electrons trapped in the magnetic field cannot fall down the
potential, and thus are extremely energetic allowing them to ionize neutral atoms. Neutral propellant is pumped into
the chamber and is ionized by the trapped electrons. Then positive ions and electrons are ejected from the thruster as
a quasineutral plasma, creating thrust.
References
Corbino disc - dashed curves represent
[1] Edwin Hall (1879). "On a New Action of the Magnet on Electric Currents" (http:/ / logarithmic spiral paths of deflected electrons
www. stenomuseet. dk/ skoletj/ elmag/ kilde9. html). American Journal of
Mathematics (American Journal of Mathematics, Vol. 2, No. 3) 2 (3): 287–92.
doi:10.2307/2369245. JSTOR 2369245. . Retrieved 2008-02-28.
[2] "The Hall Effect" (http:/ / www. eeel. nist. gov/ 812/ effe. htm). NIST. . Retrieved 2008-02-28.
[3] N.W. Ashcroft and N.D. Mermin "Solid State Physics" ISBN 978-0030839931
[4] T. Ohgaki et al. "Positive Hall coefficients obtained from contact misplacement on evident n-type ZnO films and crystals" J. Mat. Res. 23(9)
(2008) 2293 (http:/ / dx. doi. org/ 10. 1557/ JMR. 2008. 0300)
[5] Kasap, Safa. "Hall Effect in Semiconductors" (http:/ / www. webcitation. org/ 5c0UeBBsZ). Archived from the original (http:/ / mems.
caltech. edu/ courses/ EE40 Web Files/ Supplements/ 02_Hall_Effect_Derivation. pdf) on 2008-11-01. .
Hall effect 8
[6] N. A. Sinitsyn (2008). "Semiclassical Theories of the Anomalous Hall Effect" (http:/ / xxx. lanl. gov/ pdf/ 0712. 0183v2). Journal of Physics:
Condensed Matter 20: 023201. doi:10.1088/0953-8984/20/02/023201. .
[7] Adams, E. P. (1915). "The Hall and Corbino effects" (http:/ / books. google. com/ ?id=OFYLAAAAIAAJ& pg=PA47). Proceedings of the
American Philosophical Society (American Philosophical Society) 54 (216): 47–51. ISBN 9781422372562. . Retrieved 2009-01-24.
Further reading
• Classical Hall effect in scanning gate experiments: A. Baumgartner et al., Phys. Rev. B 74, 165426 (2006),
doi:10.1103/PhysRevB.74.165426
External links
Patents
• U.S. Patent 1778796 (http://www.google.com/patents?vid=1778796), P. H. Craig, System and apparatus
employing the Hall effect
General
• Interactive Java tutorial on the Hall Effect (http://www.magnet.fsu.edu/education/tutorials/java/halleffect/
index.html) National High Magnetic Field Laboratory
• Science World (wolfram.com) (http://scienceworld.wolfram.com/physics/HallEffect.html) article.
• " The Hall Effect (http://www.eeel.nist.gov/812/effe.htm)". nist.gov.
• Hall, Edwin, " On a New Action of the Magnet on Electric Currents (http://www.stenomuseet.dk/skoletj/
elmag/kilde9.html)". American Journal of Mathematics vol 2 1879.
• Spin Hall Effect Detected at Room Temperature (http://physicsweb.org/articles/news/10/9/5/1)
• Hall Effect Sensing and Application (http://content.honeywell.com/sensing/prodinfo/solidstate/technical/
hallbook.pdf). Honeywell documentation on hall effect sensing, interfacing and applications.
Article Sources and Contributors 9
License
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