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Hall effect

 
Dictionary: Hall effect
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n.
Generation of an electric potential perpendicular to both an electric current flowing along a conducting material and an external magnetic field applied at right angles to the current upon application of the magnetic field.

[After Edwin Herbert Hall (1855-1938), American physicist.]


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Britannica Concise Encyclopedia: Hall effect
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Development of a transverse electric field in a solid material carrying an electric current and placed in a magnetic field perpendicular to the current. Discovered in 1879 by Edwin H. Hall (1855 – 1938), the Hall field results from the force exerted by the magnetic field on the moving particles of the current. The Hall effect can be used to measure certain properties of current carriers as well as to detect the presence of a current on a magnetic field.

For more information on Hall effect, visit Britannica.com.

Sci-Tech Encyclopedia: Hall effect
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An effect whereby a conductor carrying an electric current perpendicular to an applied magnetic field develops a voltage gradient which is transverse to both the current and the magnetic field. It was discovered by E. H. Hall in 1879. Important information about the nature of the conduction process in semiconductors and metals may be obtained through analysis of this effect.

A simple model which accounts for the phenomenon is the following. For a magnetic field of strength B in the z direction (see illustration), particles flowing with speed v in the x direction suffer a Lorentzforce FL in the y direction given by
1. F_L = -q v B
Eq. (1), where q is the charge of the particles. This force deflects the particles so that a charge imbalance develops between opposite sides of the conductor. Deflection continues until the electric field Ey resulting from this charge imbalance produces a force Fy = qEy which cancels the Lorentz force. In practice, the equilibrium condition FL + Fy = 0 is achieved almost instantaneously, giving a steady-state Hall field as i Eq. (2). The current density is Jx = nqv, where n is the carrier density. The Hall resistivity, defined by Eq. (3), is thus given by Eq. (4). The Hall coefficient, defined by Eq. (5),
2. E_y = vB

3. \rho_{yx} =\frac{E_y}{J_x}

4. \rho_{yx} = \frac{B}{nq}

5. R_0 = \frac{\rho_{yx}}{B}
satisfies Eq. (6)
6. R_0 = \frac{1}{nq}
and thus R0 provides a measure of the sign and magnitude of the mobile charge density in a conductor. Within the free-electron theory of simple metals, q is expected to be the electron charge −e, and n is taken to be n = ZnA, where Z is the valence of the metal and nA is the density of the atoms. This yields Eq. (7).
7. R_0 = \frac{-1}{n_A Ze}
See also Free-electron theory of metals.

Configuration of fields and currents in the Hall effect experiment.
Configuration of fields and currents in the Hall effect experiment.

Equation (7) is approximately valid in simple monovalent metals but fails drastically for other materials, often even giving the wrong sign. The explanation of the failures of Eq. (7) was one of the great early triumphs of the quantum theory of solids. The theory of band structure shows how collisions with the periodic array of atoms in a crystal can cause the current carriers to be holes which have an effective positive charge which changes the sign of the Hall coefficient. Band structure theory also accounts for the observed dependence of R0 on the orientation of the current and the magnetic field relative to the crystal axes, an effect which is very useful for studying the topology of the Fermi surface. See also Band theory of solids; Fermi surface; Hole states in solids.

In certain special field-effect transistors, it is possible to create an electron gas which is effectively two-dimensional. The Hall resistance for an idealized system in two dimensions is given by Eq. (8),
8. \rho_{xy} = -\rho_{yx} = \frac{B}{n_S e}
where nS is the density of electrons per unit area (rather than volume). However, if the measured value of ρxy for a high-quality (low-disorder) device is plotted as a function of B, the linear behavior predicted by Eq. (8) is observed only at low fields. At high fields the Hall resistance exhibits plateau regions in which it is a constant independent of B. Furthermore, the values of ρxy on these plateaus are given quite accurately by the universal relation of Eq. (9),
9. \rho_{xy} = \frac{h}{e^2 \nu}
where h is Planck's constant and ν is an integer or simple rational fraction. The absolute accuracy with which Eq. (9) has been verified is better than 1 part in 106.

This extremely accurate quantization of ρxy allows the realization of a new standard of resistance based solely on fundamental constants of nature. In addition, the quantum unit of Hall resistance, h/e2 ≃ 25,812.80 ohms, determines the fine-structure constant. See also Electrical units and standards; Fundamental constants.

The explanation of this remarkable phenomenon involves several subtle quantum-mechanical effects. In the quantum regime (small ν), ρxx, which is the dissipative (longitudinal) resistivity, approaches zero on the Hall plateaus. The quantization of the Hall resistance is intimately connected with this fact. It is speculated that at zero temperature the dissipation is zero and that Eq. (9) is then obeyed exactly. See also Quantum mechanics.

The nearly complete lack of dissipation in the quantum Hall regime is reminiscent of superconductivity. In both effects the ability of the current to flow without dissipation has its origin in the existence of a quantum-mechanical excitation gap, that is, a minimum threshold energyneeded to disturb the special microscopic order in the system. See also Entropy; Superconductivity.

In the integer quantum Hall effect [where ν in Eq. (9) in an integer], this excitation gap is a single-particle effect associated with the quantization by the strong magnetic field of the kinetic energy of the individual electrons into discretestates called Landau levels. In the fractional effect, the gap is associated with the highly collective, many-body ordering of the electrons into a quantum state which minimizes the strong Coulomb repulsion and hence lowers the overall energy. Thus, while the integer and fractional quantum Hall effects look superficially similar on a plot of resistivities versus magnetic field,their physical origins are actually quite different. See also Galvanomagnetic effects.

 
Columbia Encyclopedia: Hall effect
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Hall effect, experiment that shows the sign of the charge carriers in a conductor. In 1879 E. H. Hall discovered that when he placed a metal strip carrying a current in a magnetic field, a voltage difference was produced across the strip. The side of the strip that is at the higher voltage depends on the sign of the charge carrier; Hall's work demonstrated that in metals the charge carriers are negative. Today it is known that this negative charge carrier is the electron. The Hall effect has again become an active area of research with the discovery of the quantized Hall effect, for which Klaus von Klitzing was awarded the 1985 Nobel Prize in physics. Before von Klitzing's work it was thought that the amount of voltage difference across the strip varied in direct proportion to the strength of the magnetic field-the greater the magnetic field, the greater the voltage difference. Von Klitzing showed that under the special conditions of low temperature, high magnetic field, and two-dimensional electronic systems (in which the electrons are confined to move in planes), the voltage difference increases as a series of steps with increasing magnetic field.

Wikipedia: Hall effect
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Hall effect diagram, showing electron flow (rather than conventional current).
Legend:
1. Electrons (not conventional current!)
2. Hall element, or Hall sensor
3. Magnets
4. Magnetic field
5. Power source
Description
In drawing "A", the Hall element takes on a negative charge at the top edge (symbolised by the blue color) and positive at the lower edge (red color). In "B" and "C", either the electric current or the magnetic field is reversed, causing the polarization to reverse. Reversing both current and magnetic field (drawing "D") causes the Hall element to again assume a negative charge at the upper edge.

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. Edwin Hall discovered this effect 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, as its value depends on the type, number and properties of the charge carriers that constitute the current.

Contents

Discovery

The Hall effect was discovered in 1879 by Edwin Herbert Hall while working on his doctoral degree at the Johns Hopkins University in Baltimore, Maryland, USA. 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, or both. Moving charges experience a force, called the Lorentz Force, when a magnetic field is present that is not parallel to their motion.[2] 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 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.

Hall-effect.png

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}{dne}

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

R_H =\frac{E_y}{j_xB}

where j is the current density of the carrier electrons. In SI units, this becomes

R_H =\frac{E_y}{j_xB}= \frac{dV_H}{IB}=-\frac{1}{ne}

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. However, the actual electrons that correspond to the fictional "holes" have negative Effective mass, and thus are deflected in the opposite direction [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]

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 the magnetic field and 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 coefficient is[5]

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 absolute value of the electronic charge.

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

R_H=\frac{(p-nb^2)}{e(p+nb)^2}

with b=\frac{\mu_e}{\mu_h}

Technological 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, fluid flow sensors, current sensors, and pressure sensors. Other applications may be found in some electric airsoft guns and on the triggers of electropneumatic paintball guns, as well as current smart phones, and some global positioning systems.

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, which is the quantization of the Hall voltage.

Spin Hall effect

Main article: Spin Hall effect

The Spin 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 temperatures.

Quantum Spin Hall effect

Main article: 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.

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.) 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).[6]

Hall effect in ionized gases

(See electrothermal instability)

The Hall effect in an ionized gas (plasma) is significantly different from the Hall effect in solids (where the Hall parameter is always very inferior to 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 frequency, ν:

\beta=\frac {\Omega_e}{\nu}=\frac {eB}{m_e\nu}

where

e is the elementary charge (approx. 1.6 × 10-19 C)
B is the magnetic field (in tesla)
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:

β = tan(θ)

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 in fact contain 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. 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.

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 electromechanical sensing.

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.

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 pussyhole 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. 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 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. CZV

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.

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 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.

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

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 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 and semiconductor 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. It is worth noting that 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 though the signal output wire.

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.

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 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 magnetic field is used to trap the ionized electrons. After the positive ions are accelerated by the electric field, trapped electrons are recaptured by the positive ions and result in fast neutral atoms exiting the HET and providing thrust. Neutralizing the ions eliminates the electrostatic attraction that positively charged ions would have had for the electrons that they left behind. Thus the neutral atoms propelled out the rear won't exert an attractive electrostatic force on the spacecraft, which would have partly canceled the forward propulsion.

The Corbino effect

The Corbino effect is a phenomenon similar to the Hall effect, but a disc-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 disc, produces a "circular" current through the disc.[7]

The absence of the free transverse boundaries render the interpretation of the Corbino effect simpler than that of the Hall effect.

See also

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References

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 This article needs additional citations for verification.
Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (January 2008)
  1. ^ Edwin Hall (1879). "On a New Action of the Magnet on Electric Currents". American Journal of Mathematics 2: 287–92. doi:10.2307/2369245. http://www.stenomuseet.dk/skoletj/elmag/kilde9.html. Retrieved 2008-02-28. 
  2. ^ "The Hall Effect". NIST. http://www.eeel.nist.gov/812/effe.htm. Retrieved 2008-02-28. 
  3. ^ Lianxi Ma, Qingli Zhao, Chi Chen. 2009. Holes in Hall Effect. Lat. Am. J. Phys. Edu. Vol 3 No 1 [1]
  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
  5. ^ Kasap, Safa. "Hall Effect in Semiconductors". Archived from the original on 2008-11-01. http://www.webcitation.org/5c0UeBBsZ. 
  6. ^ N. A. Sinitsyn (2008). "Semiclassical Theories of the Anomalous Hall Effect". Journal of Physics: Condensed Matter 20: 023201. doi:10.1088/0953-8984/20/02/023201. http://xxx.lanl.gov/pdf/0712.0183v2. 
  7. ^ Adams, E. P. (1915). "The Hall and Corbino effects". Proceedings of the American Philosophical Society 54 (216): 47–51. http://books.google.com/books?hl=en&lr=&id=OFYLAAAAIAAJ&oi=fnd&pg=PA47&ots=SoPL26jU8r&sig=WZUP2c3OdQ_EFIthAzXY87dp7kE. Retrieved 2009-01-24. 

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Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
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