[pic]TERM PAPER

WAVES, ELECTRICITY AND MAGNETISM

PHY111

Topic: Cross Field and its application (Hall Effect)

DOA: 18-02-2010

DOR:11-03-2010

DOS: 05-05-2010

Submitted to:-

Mr.Jagmohan Rana Submitted by:-

Shailendra Singh

Roll No:-A06

Section:-B4902

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ACKNOWLEDGEMENT

It is not until you undertake the term paper like this one that you realize how massive the effort it really is, or how much you must rely upon the Selfless efforts and goodwill of others. There are many who helped us with this term paper, and we want to thank them all from the core of our Hearts.

We owe special words of thanks to our Teacher Mr.Jagmohan Rana for her vision, thoughtful counseling and encouragement at every step of the project. I am also thankful to the teachers of the Department for giving us the best of knowledge and guidance throughout the term paper. And last but not the least, we find no words to acknowledge the financial assistance & moral support rendered by our parents in making the effort a success. All this has become reality because of their blessings and above all by the grace of god.

• CERTIFICATE:-
This is to certify that the project entitled “Hall Effect” submitted by SHAILENDRA SINGH has been carried out under our supervision. The project is submitted in fulfillment of the requirement for the 2nd semester of B.TECH ( ME).

• Contents:-
1-Introduction of Hall Effect
2-Invention of Hall Effect
3-Illustration of Hall Effect
4-History

5-Types of Hall Effect

a) Quantum Hall effect b) Spin Hall effect c) Anomalous Hall Effect d) Thermal effect
6- Effects of Hall Effect
7- Applications
8- Advantages over other methods
9- References • Introduction to 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. Edwin Hall discovered this effect in 1879.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.
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• Invention of Hall Effect:-
The Hall effect was discovered in 1879 by Edwin He 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.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.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. • Illustration of Hall effect:-
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 perpendicular 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 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.
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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 [pic] 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 [pic] where j is the current density of the carrier electrons. In SI units, this becomes [pic]
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
It must be noted though that the sample in homogeneity 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.

History:-

The Hall effect was discovered by Edwin Hall in 1879 when he was a graduate student in the Johns Hopkins University under the advisory of Professor Henry A. Rowland, after whose name this department is named now. But at that time, even the electron was not experimentally discovered. Clear understanding had to wait until quantum mechanics came into apperance.
In 1930, Landau showed that for quantum electrons, unlike classical electrons, the electron's orbital motion gave a contribution to the magnetic susceptibility. He also remarked that the kinetic energy quantization gave rise to a contribution to the magnetic susceptibility which was periodic in inverse magnetic field. We can see later that Landau levels along with localization can explain the integer quantum Hall effect satisfactorily.
The first inversion layer Hall conductivity measurements in strong magnetic fields were done by S.Kawaji and his colleagues in 1975. Using a somewhat different experimental arrangement which measured the Hall voltage rather than the Hall current, Klaus von Klitzing and Th. Egbert found flat Hall plateaus in 1978. However, the precise quantization of the Hall conductance in units of [pic] was not recognized until February of 1980. Five years later, in 1985, Klaus von Klitzing was awarded Nobel Prize in Physics for the discovery of quantum Hall effect.

Types of Hall Effect:-

1-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.
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[pic] 2-Spin Hall Effect:-
The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional, semiconductors with spin-orbit coupling. The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, but, unlike the latter, it does not require the application of a large magnetic field. The quantum spin Hall state does not break any discrete symmetries (such as time-reversal or parity). It has been recently proposed and subsequently experimentally realized in mercury (II) telluride (HgTe) semiconductors.
The first proposal for the existence of a quantum spin Hall state was developed by Kane and Male who adapted an earlier model for graphene by Haldane which exhibits an integer quantum Hall effect. The Kane and Mele model is two copies of the Haldane model such that the spin up electron exhibits a chiral integer quantum Hall Effect while the spin down electron exhibits and anti-chiral integer quantum Hall effect. Overall this idealized model has a charge-Hall conductance of exactly zero but a spin-Hall conductance of exactly . Independently, a quantum spin Hall model was proposed by Bernevig and Zhang in an intricate strain architecture which engineers, due to spin-orbit coupling, a magnetic field pointing upwards for spin-up electrons and a magnetic field pointing downwards for spin-down electrons. The main ingredient is the existence of spin-orbit coupling, which can be understood as a momentum-dependent magnetic field coupling to the spin of the electron.
Strictly speaking, the models with spin-orbit coupling do not have a quantized spin Hall conductance [pic]. Those models are more properly referred as topological insulator which is an example of topologically ordered states.
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3-Quantum spins Hall Effect
For Hg Te 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.
In the gap closing and re-opening process, two edge states are brought out from the bulk and cross the bulk-gap. As such, when the Fermi level resides in the bulk gap, the conduction is dominated by the edge channels that cross the gap. The two-terminal conductance is in the quantum spin Hall state and zero in the normal insulating state. As the conduction is dominated by the edge channels, the value of the conductance should be insensitive to how wide the sample is. A magnetic field should destroy the quantum spin Hall state by breaking time-reversal invariance and allowing spin-up spin-down electron scattering processes at the edge. All these predictions have been experimentally verified in an experiment erformed in the Molenkamp labs at Universidad Wurzburg in Germany 4-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).
5-Thermal effect:-
The thermal Hall effect is the thermal analog of the Hall effect. Here, a thermal gradient is produced across a solid instead of an electric field. When a magnetic field is applied, an orthogonal temperature gradient develops.
For conductors, a significant portion of the thermal current is carried by the electrons. In particular, the Righi–Leduc Effect describes the heat flow resulting from a perpendicular temperature gradient and vice versa, and the Maggi–Righi–Leduc effect describes changes in thermal conductivity when placing a conductor in a magnetic field.
A thermal Hall effect has also been measured in a paramagnetic insulator and dubbed the "phonon Hall effect."[1] In this case, there are no charged currents in the solid so the magnetic field cannot exert a Lorentz force. An analogous thermal Hall effect for neutral particles exists in polyatomic gases (known as the Senftleben-Beenakker effect). • Effects of Hall Effect:-
1-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 coefficient is [pic] where [pic]is the electron concentration, [pic]the hole concentration, [pic]the electron mobility , [pic]the hole mobility and [pic]the absolute value of the electronic charge.
For large applied fields the simpler expression analogous to that for a single carrier type holds. [pic] with [pic]
2-Hall Effect in ionized gases
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: [pic] 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: β = tan(θ)

3-Charge Carriers in the Hall Effect:-

The Hall Effect is a conduction phenomenon which is different for different charge carriers. In most common electrical applications, the conventional current is used partly because it makes no difference whether you consider positive or negative charge to be moving. But the Hall voltage has a different polarity for positive and negative charge carriers, and it has been used to study the details of conduction in semiconductors and other materials which show a combination of negative and positive charge carriers.
The Hall Effect can be used to measure the average drift velocity of the charge carriers by mechanically moving the Hall probe at different speeds until the Hall voltage disappears, showing that the charge carriers are now not moving with respect to the magnetic field. Other types of investigations of carrier behavior are studied in the quantum Hall effect. • 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 as described above plus a high gain integrated circuit (IC) amplifier in a single package. Recent advances have further added into one package an ADC (Analog to Digital) converter and I²C (Inter-integrated circuit communication protocol) IC for direct connection to a microcontroller's I/O port.
Hall probes are often used to measure magnetic fields, or inspect materials (such as tubing or pipelines) using the principles of magnetic flux leakage. • 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 electro pneumatic paintball guns, as well as current smart phones, and some global positioning systems. • 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.
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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 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 feed through 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
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• References:- 1- http://www.stenomuseet.dk/skoletj/elmag/kilde9.html.. 2- http://www.eeel.nist.gov/812/effe.htm. 3- http://www.webcitation.org/5c0UeBBsZ. 4- http://books.google.com/books?hl=en&lr=&id=OFYLAAAAIAAJ&oi=fnd&pg=PA4&ots=SoPL26jU8r&sig=WZUP2c3OdQ_EFIthAzXY87dp7kE. 5- http://xxx.lanl.gov/pdf/0712.0183v2.
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