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 to an applied magnetic field
perpendicular to the current. It was discovered by
Edwin Hall in
1879. For clarity, the original effect is sometimes called the
Hall effect to distinguish it from other "Hall effects" which
have different physical mechanisms.
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.
Hall effect in semiconductors
2.2 Relationship with star formation
2.3 Quantum Hall effect
2.4 Spin Hall effect
2.5 Quantum spin Hall effect
2.6 Anomalous Hall effect
Hall effect in ionized gases
3.1 Advantages over other methods
3.2 Disadvantages compared with other methods
3.3 Contemporary applications
3.3.1 Ferrite toroid
Hall effect current transducer
3.3.2 Split ring clamp-on sensor
3.3.3 Analog multiplication
3.3.4 Power measurement
3.3.5 Position and motion sensing
3.3.6 Automotive ignition and fuel injection
3.3.7 Wheel rotation sensing
3.3.8 Electric motor control
3.3.9 Industrial applications
4 The Corbino effect
5 See also
8 Further reading
9 External links
Hall effect was discovered in 1879 by
Edwin Hall while he was
working on his doctoral degree at
Johns Hopkins University
Johns Hopkins University in
Baltimore, Maryland. Eighteen years before the electron was
discovered, his measurements of the tiny effect produced in the
apparatus he used were an experimental tour de force, published under
the name "On a New Action of the Magnet on Electric Currents".
Hall effect is 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.
When a magnetic field is present, these charges experience a force,
called the Lorentz force. 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 magnetic
field with a perpendicular component is applied, their paths between
collisions are curved, thus 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,
arising from a force 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 electric potential is established for as long as
the charge is flowing.
In classical electromagnetism electrons move in the opposite direction
of the current I (by convention "current" describes a theoretical
"hole flow"). In some semiconductors it appears "holes" are actually
flowing because the direction of the voltage is opposite to the
Hall effect measurement setup for electrons. Initially, the electrons
follow the curved arrow, due to the magnetic force. At some distance
from the current-introducing contacts, electrons pile up on the left
side and deplete from the right side, which creates an electric field
ξy in the direction of the assigned VH. VH is negative for some
semiconductors where "holes" appear to flow. In steady-state, ξy will
be strong enough to exactly cancel out the magnetic force, thus the
electrons follow the straight arrow (dashed).
Animation showing the simplified principle
For a simple metal where there is only one type of charge carrier
(electrons), the Hall voltage VH can be derived by using the Lorentz
force and seeing that, in the steady-state condition, charges are not
moving in the y-axis direction. Thus, the magnetic force on each
electron in the y-axis direction is cancelled by a y-axis electrical
force due to the buildup of charges. The vx term is the drift velocity
of the current which is assumed at this point to be holes by
convention. The vxBz term is negative in the y-axis direction by the
right hand rule.
displaystyle mathbf F =q bigl ( mathbf E +(mathbf v times
mathbf B ) bigl )
In steady state, F = 0, so 0 = Ey − vxBz, where Ey is assigned in
the direction of the y-axis, (and not with the arrow of the induced
electric field ξy as in the image (pointing in the −y direction),
which tells you where the field caused by the electrons is pointing).
In wires, electrons instead of holes are flowing, so vx → −vx and
q → −q. Also Ey = −VH/w. Substituting these changes gives
displaystyle V_ mathrm H =v_ x B_ z w
The conventional "hole" current is in the negative direction of the
electron current and the negative of the electrical charge which gives
Ix = ntw(−vx)(−e) where n is charge carrier density, tw is the
cross-sectional area, and −e is the charge of each electron. Solving
and plugging into the above gives the Hall voltage:
displaystyle V_ mathrm H = frac I_ x B_ z nte
If the charge build up had been positive (as it appears in some
semiconductors), then the VH assigned in the image would have been
negative (positive charge would have built up on the left side).
The Hall coefficient is defined as
displaystyle R_ mathrm H = frac E_ y j_ x B_ z
where j is the current density of the carrier electrons, and Ey is the
induced electric field. In SI units, this becomes
displaystyle R_ mathrm H = frac E_ y j_ x B = frac V_
mathrm H t IB =- frac 1 ne .
(The units of RH are usually expressed as m3/C, or Ω·cm/G, or other
variants.) 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
The sample inhomogeneity might result in spurious sign of the Hall
effect, even in ideal van der Pauw configuration of electrodes. For
Hall effect was observed in evidently n-type
semiconductors. Another source of artifact, in uniform materials,
occurs when the sample's aspect ratio is not long enough: the full
Hall voltage only develops far away from the current-introducing
contacts, since at the contacts the transverse voltage is shorted out
Hall effect in semiconductors
When a current-carrying semiconductor is kept in a magnetic field, the
charge carriers of the semiconductor experience a force in a direction
perpendicular to both the magnetic field and the current. At
equilibrium, a voltage appears at the semiconductor edges.
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
displaystyle R_ mathrm H = frac pmu _ mathrm h ^ 2 -nmu _
mathrm e ^ 2 eleft(pmu _ mathrm h +nmu _ mathrm e right)^ 2
displaystyle R_ mathrm H = frac left(p-nb^ 2 right)
displaystyle b= frac mu _ mathrm e mu _ mathrm h
Here n is the electron concentration, p the hole concentration, μe
the electron mobility, μh the hole mobility and e the elementary
For large applied fields the simpler expression analogous to that for
a single carrier type holds.
Relationship with star formation
Although it is well known that magnetic fields play an important role
in star formation, research models indicate that Hall
diffusion critically influences the dynamics of gravitational collapse
that forms protostars.
Quantum Hall effect
Main article: Quantum Hall effect
For a two-dimensional electron system which can be produced in a
MOSFET, in the presence of large magnetic field strength and low
temperature, one can observe the quantum Hall effect, in which the
Hall conductance σ undergoes quantum Hall transitions to take on the
Spin Hall effect
Main article: Spin Hall effect
Hall effect consists in the spin accumulation on the lateral
boundaries of a current-carrying sample. No magnetic field is needed.
It was predicted by M. I. Dyakonov and V. I. Perel in 1971 and
observed experimentally more than 30 years later, both in
semiconductors and in metals, at cryogenic as well as at room
Quantum spin Hall effect
Main article: Quantum spin Hall effect
For mercury telluride two dimensional quantum wells with strong
spin-orbit coupling, in zero magnetic field, at low temperature, the
Hall effect has been recently observed.
Anomalous Hall effect
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.) For example, in nickel, the anomalous Hall
coefficient is about 100 times larger than the ordinary Hall
coefficient near the Curie temperature, but the two are similar at
very low temperatures. Although a well-recognized phenomenon,
there is still debate about its origins in the various materials. The
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).
Hall effect in ionized gases
Hall effect in an ionized gas (plasma) is significantly different
Hall effect in solids (where the Hall parameter is always
much less than unity). In a plasma, the Hall parameter can take any
value. The Hall parameter, β, in a plasma is the ratio between the
electron gyrofrequency, Ωe, and the electron-heavy particle collision
displaystyle beta = frac Omega _ mathrm e nu = frac eB
m_ mathrm e nu
e is the elementary charge (approximately
B is the magnetic field (in teslas)
me is the electron mass (approximately
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 longer collinear
with the electric field vector, E. The two vectors J and E make the
Hall angle, θ, which also gives the Hall parameter:
displaystyle beta =tan(theta ).
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
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.
Advantages over other methods
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
Hall effect current sensor with internal integrated circuit amplifier.
8 mm opening. Zero current output voltage is midway between the supply
voltages that maintain a 4 to 8 volt differential. Non-zero current
response is proportional to the voltage supplied and is linear to 60
amperes for this particular (25 A) device.
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.
Disadvantages compared with other methods
Magnetic flux from the surroundings (such as other wires) may diminish
or enhance the field the
Hall probe intends to detect, rendering the
results inaccurate. Also, as Hall voltage is often on the order of
millivolts, the output from this type of sensor cannot be used to
directly drive actuators but instead must be amplified by a
Ways to measure component positions within an electromagnetic system,
such as a brushless direct current motor, include (1) the Hall effect,
(2) light detection with a light-dark position encoder such as a Gray
code disk and (3) induced voltage by moving the amount of metal core
inserted into a transformer. When Hall is compared to photo-sensitive
methods, it is harder to get absolute position with Hall. Hall
detection is also sensitive to stray magnetic fields.
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
Hall effect current transducer
Hall effect current transducer integrated into ferrite
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 the
detection of stray fields by a factor of 100 or better (as the
external magnetic fields cancel across the ring, giving no residual
magnetic flux). 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, each turn adding to the sensor output the same quantity; when
the sensor is installed onto a printed circuit board, the turns can be
carried out by a staple on the board. 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
Multiple 'turns' and corresponding transfer function.
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 electric current to be tested without dismantling the existing
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 digital
computers, the remaining useful application is in power sensing, which
combines current sensing with voltage sensing in a single Hall effect
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.
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. This application is used in
brushless DC motors.
Automotive ignition and fuel injection
Commonly used in distributors for ignition timing (and in some types
of crank and camshaft position sensors for injection pulse timing,
speed sensing, etc.) the
Hall effect sensor
Hall effect sensor is used as a direct
replacement for the mechanical breaker points used in earlier
automotive applications. Its use as an ignition timing device in
various distributor types is as follows. A stationary permanent magnet
Hall effect chip are mounted next to each other
separated by an air gap, forming the
Hall effect sensor. A metal rotor
consisting of windows and tabs is mounted to a shaft and arranged so
that during shaft rotation, the windows and tabs pass through the air
gap between the permanent magnet and semiconductor Hall chip. This
effectively shields and exposes the Hall chip to the permanent
magnet's field respective to whether a tab or window is passing though
the Hall sensor. For ignition timing purposes, the metal rotor will
have a number of equal-sized tabs and windows matching the number of
engine cylinders. This produces a uniform square wave output since the
on/off (shielding and exposure) time is equal. This signal is used by
the engine computer or ECU to control ignition timing. Many automotive
Hall effect sensors have a built-in internal NPN transistor with an
open collector and grounded emitter, meaning that rather than a
voltage being produced at the Hall sensor signal output wire, the
transistor is turned on providing a circuit to ground through the
signal output wire.
Wheel rotation sensing
The sensing of wheel rotation is especially useful in anti-lock
braking systems. The principles of such systems have been extended and
refined to offer more than anti-skid functions, now providing extended
vehicle handling enhancements.
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. This allows for more precise motor control
Hall effect sensing have also expanded to industrial
applications, which now use
Hall effect joysticks to control hydraulic
valves, replacing the traditional mechanical levers with contactless
sensing. Such applications include mining trucks, backhoe loaders,
cranes, diggers, scissor lifts, etc.
Hall-effect thruster (HET) is a relatively low power device that is
used to propel some spacecraft, after it gets 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 drop to the lower potential. They
are thus extremely energetic, which means that they can ionize neutral
atoms. Neutral propellant is pumped into the chamber and is ionized by
the trapped electrons. Positive ions and electrons are then ejected
from the thruster as a quasineutral plasma, creating thrust.
The Corbino effect
Corbino disc – dashed curves represent logarithmic spiral paths of
The Corbino effect is a phenomenon involving the Hall effect, but a
disc-shaped metal sample is used in place of a rectangular one.
Because of its shape the Corbino disc allows the observation of Hall
effect–based magnetoresistance without the associated Hall voltage.
A radial current through a circular disc, subjected to a magnetic
field perpendicular to the plane of the disc, produces a "circular"
current through the disc.
The absence of the free transverse boundaries renders the
interpretation of the Corbino effect simpler than that of the Hall
Coulomb potential between two current loops embedded in a magnetic
List of plasma (physics) articles
Quantum Hall effect
Fractional quantum Hall effect
Quantum anomalous Hall effect
Spin Hall effect
Thermal Hall effect
Edwin Hall (1879). "On a New Action of the Magnet on Electric
Currents". American Journal of Mathematics. 2 (3): 287–92.
doi:10.2307/2369245. JSTOR 2369245. Archived from the original on
2011-07-27. Retrieved 2008-02-28.
^ Bridgeman, P. W. (1939). Biographical Memoir of Edwin Herbert Hall.
National Academy of Sciences.
^ "Hall Effect History". Retrieved 2015-07-26.
^ Ramsden, Edward (2006). Hall-Effect Sensors. Elsevier Inc.
pp. xi. ISBN 978-0-7506-7934-3.
^ "The Hall Effect". NIST. Retrieved 2008-02-28.
^ N.W. Ashcroft and N.D. Mermin "Solid State Physics"
^ 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
^ Kasap, Safa. "Hall Effect in Semiconductors". Archived from the
original (PDF) on 2008-11-01.
^ Mark Wardle (2004). "Star Formation and the Hall Effect".
Astrophysics and Space Science. 292 (1): 317–323.
arXiv:astro-ph/0307086 . Bibcode:2004Ap&SS.292..317W.
doi:10.1023/B:ASTR.0000045033.80068.1f. Retrieved 2015-12-20.
^ Braiding, Catherine R & Wardle, Mark (2012) "The
Hall effect in
star formation", Macquarie University, Australia
^ Braiding, Catherine R & Wardle, Mark (2012) "The
Hall effect in
accretion flows", Macquarie University, Australia
^ Robert Karplus and J. M. Luttinger (1954). "Hall Effect in
Ferromagnetics". Phys. Rev. 95 (5): 1154–1160.
^ N. A. Sinitsyn (2008). "Semiclassical Theories of the Anomalous Hall
Effect". Journal of Physics: Condensed Matter. 20 (2): 023201.
arXiv:0712.0183 . Bibcode:2008JPCM...20b3201S.
^ Adams, E. P. (1915). "The Hall and Corbino effects". Proceedings of
the American Philosophical Society. American Philosophical Society. 54
(216): 47–51. ISBN 978-1-4223-7256-2. Retrieved
Introduction to Plasma Physics and Controlled Fusion, Volume 1, Plasma
Physics, Second Edition, 1984, Francis F. Chen
Hall effect in scanning gate experiments: A. Baumgartner et
al., Phys. Rev. B 74, 165426 (2006), doi:10.1103/PhysRevB.74.165426
Annraoi M. de Paor. Correction to the classical two-species Hall
Coefficient using twoport network theory. International Journal of
Electrical Engineering Education 43/4.
U.S. Patent 1,778,796, P. H. Craig, System and apparatus employing the
U.S. Patent 3,596,114, J. T. Maupin, E. A. Vorthmann, Hall effect
contactless switch with prebiased Schmitt trigger
Understanding and Applying the Hall Effect
Hall Effect Thrusters Alta Space
Hall effect calculators
Interactive Java tutorial on the
Hall effect National High Magnetic
Science World (wolfram.com) article.
"The Hall Effect". nist.gov.
Table with Hall coefficients of different elements at room
Simulation of the
Hall effect as a Youtube video
Hall effect in electrolytes
Bowley, Roger (2010). "Hall Effect". Sixty Symbols.
Brady Haran for
the University of Nottingham.