Hall Effect Presentation

Edwin Herbert Hall Edwin Herbert Hall Edwin Herbert Hall Edwin Herbert Hall

November 7, 1855 - November 20, 1938)

was American physicist who was American physicist who was American physicist who was American physicist who discovered in 1879 the "Hall effect”discovered in 1879 the "Hall effect”discovered in 1879 the "Hall effect”discovered in 1879 the "Hall effect”

� Edwin Herbert Hall discovered the "Hall effect" in 1879 whileworking on his doctoral thesis in Physics under thesupervision of Professor Henry Augustus Rowland.

� Hall was pursuing the question first posed by Maxwell as to◦ whether the resistance of a coil excited by a current was affected by the

presence of a magnet.presence of a magnet.

◦ Does the force act on the conductor or the current?

� Hall argued that if the current was affected by the magneticfield then there should be "a state of stress... the electricitypassing toward one side of the wire."

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� Through a myriad of experiments and failures, Halldiscovered that a magnetic field would skew equipotentiallines in a current-carrying conductor. This effect is observedas a voltage (Hall voltage) perpendicular to the direction ofcurrent in the conductor.

� Hall conducted an experiment by putting a thin gold leaf on aglass plate and then tapping off the gold leaf at points downits length. He then conducted other experiments usingvarious materials in place of the gold leaf, and variousexperimental placements of tapping points.


� In 1880, full details of Hall's experimentation with thisphenomenon formed his doctoral thesis and was published inthe American Journal of Science and in the PhilosophicalMagazine. ( "On a New Action of the Magnet on ElectricalCurrent" )

The electron, for instance, was not identified until more than� The electron, for instance, was not identified until more than10 years later.

� Provides a simple method for accurately measuring carrierdensity, electrical resistivity, and the mobility of carriers insemiconductors


� The LeftLeftLeftLeft HandHandHandHand RuleRuleRuleRule shows what happens when chargedparticles (such as electrons in a current) enter a magneticfield


� A charged particle moving through a magnetic fieldexperiences a force that is at right angles to both thedirection in which the particle is moving and the direction ofthe applied field. This force, known as the LorentzLorentzLorentzLorentz forceforceforceforce,develops due to the interaction of the applied magnetic fieldand the magnetic field generated by the particle in motion.

� The phenomenon is named for Dutch physicist HendrikHendrikHendrikHendrikLorentzLorentzLorentzLorentz, who developed an equation that mathematicallyrelates the force to the velocity and charge of the particle andthe strength of the applied magnetic field.


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Hall Field

� Electrical currents are affected by magnetic fields. When amagnetic field is applied perpendicular to the flow of current,the field causes resistance in the current. This is amanifestation of the Lorentz force, which pushes thenegatively charged electrons in the current in a directiondictated by the left hand rule. Hall Force completely cancels the Lorentz Force

FH=FLFH=FL


At steady stateFe=Fm

� This movement of electrons results in a weak but measurablepotentialpotentialpotentialpotential differencedifferencedifferencedifference, or voltagevoltagevoltagevoltage, perpendicular both to thecurrent flow and the applied magnetic field.

� This is known as the HallHallHallHall effecteffecteffecteffect, named after Americanphysicist Edwin Hall, who discovered the phenomenon in1879.1879.

� This effect is particularly pronounced in thin metals, and iseasily observable in a low-density plasma (an electricallyconductive ionized gas), such as a fluorescent light, as in thistutorial.


� Hall Force (which opposes Lorentz force) completely cancelsthe Lorentz Force FH=FL:

oror

� Which is the Hall field. It is convenient to express this interms of measurable quantities, and for this purpose thevelocity is expressed in terms of the current density

. This leads to


� The hall field is thus proportional both to the current and tothe magnetic field. The proportionality constant – that is,

is known as the , and is usuallydenoted bydenoted by

� We can determine electron concentration n from the hall field.


� A similar effect is seen in semiconductors, where the Halleffect plays a large role in the design of integrated circuits onsemiconductor chips. In mostmostmostmost conductorsconductorsconductorsconductors, such as metals, theHallHallHallHall effecteffecteffecteffect isisisis veryveryveryvery smallsmallsmallsmall because the density of conduction inelectrons is very large and the drift speed (charged particleerraticism) is extremely small, even for the highest obtainablecurrent densities. The Hall effect is therefore consideredunimportant in most electric circuits and devices and is notunimportant in most electric circuits and devices and is notmentioned in many texts on electricity and magnetism.

� However,However,However,However, inininin semiconductorssemiconductorssemiconductorssemiconductors and in most laboratory plasmas,the current density is many orders of magnitude smaller thanin metals, and the Hall effect is correspondingly larger and isoften easily observable. Some devices for measuring magneticfields make use of semiconductors as the sensing elementsand are called HallHallHallHall probesprobesprobesprobes.


Hall Constants (in volt m3/ amp weber at RT)

Li

-1.7x

10

Na

-2.50

Cu

-0.55

Ag

-0.84

Au

-0.72

Zn

+0.3

Cd

+0.6

Al

-0.3010-10

-2.50 -0.55 -0.84 -0.72 +0.3 +0.6 -0.30


Sign depends on the sign of the charge of the current carriers. Thus Electrons, being negatively charged, lead to a negative Hall constant.

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

� The Hall coefficient is defined as

� 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 itdifferentiates between positive charges moving in onedirection and negative charges moving in the opposite.

� The Hall effect offered the first real proof that electriccurrents in metals are carried by moving electrons, not byprotons.protons.

� The Hall effect also showed that in some substances(especially semiconductors), it is more appropriate to think ofthe current as positive "holes" moving rather than negativeelectrons.


� Hall coefficient formula becomes more complex insemiconductors where the carriers are generally bothelectrons and holes which may be present in differentconcentrations and have different mobilities. For moderatemagnetic fields the Hall coefficient is

� where n is the electron concentration, p the holeconcentration, �e the electron mobility , �h the hole mobilityand e is the electronic charge.


� For large applied fields the simpler expression analogous tothat for a single carrier type holds.


� The number of conduction electrons per unit volume (N) is found by:

Where Ix= current, Bz= magnetic field, d=sample thickness, e= elementary charge, VH=Hall voltage in the y-direction

� The Hall Resistance, or Hall constant, (RH) is often defined:

Important EquationsImportant EquationsImportant EquationsImportant EquationsImportant EquationsImportant EquationsImportant EquationsImportant Equations

N =IxBz

edVH

RH=1

Ne

� Thus, the Hall voltage (VH) can be written as:

� Then, the Hall mobility (µ) can be determined:

Where Rs is the sheet resistance, easily determined by the van der Pauw method

VH=IxBz

Ned= I

xRH

Bz

d

µ =VH

RsIxBz

=1

RsNde


� Usefulness:◦ Resistance and conductance were used for characterization in the

early 1800’s, but they are influenced by sample geometry and are not material properties.

◦ For comparison between samples with different geometries, resistivity and conductivity were used. However, they are still not material properties.

◦ The Hall Effect allows measurement of carrier density and mobility, which are material properties, giving a deeper level of understanding

• Advantages:

– Simple, low-cost, fast turn-around time

– High sensitivity: Can measure carrier concentrations in doped silicon of <1012 e-/cm3

which are material properties, giving a deeper level of understanding of materials.

References: 2, 3, 7.


� Ohmic contacts:

◦ Symmetric placement on sample

• Sample geometry:– Sample uniformity

– Accurate thickness determination

– Lateral dimensions must be large compared to contact size and sample thickness

◦ Symmetric placement on sample

◦ Size

◦ Quality

� Thermomagnetic effects

� Photoconductive and photovoltaic effects

� Accurate measurement of sample temperature, intensity of magnetic field, electrical current, and voltage

Reference: 3.


• Hall Effect sensors for sensing position, motion, magnetic fields fluid flow, power, or pressure– Long life (30 billion operations, in some

tests)

– High speed operation (> 100 kHz possible)

– Highly repeatable operation

– Stationary operation (no moving parts)

– Compatible input/output for logic devices)

Hall effect current sensor.Dimensions≈ 30x15x11mm.

� Industrial and commercial use: ◦ Electronics industry: Manufacturing low-noise transistors, electronic

compasses

◦ Automobile Industry: Fuel injection systems and anti-lock brake systems

◦ Computers: Brushless DC rotors and disk-drive index sensors

◦ In general:

� Hydraulic controls

� Integration into magnetic shields to reduce stray fields

� Inspect tubing or pipelines for corrosion or pitting

devices)30x15x11mm.


(1) Kittel, Charles. Introduction to Solid State Physics. 6th edition. New York: John Wiley & Sons, Inc., 1986.

(2) Hummel, Rolf. E. Electronic Properties of Materials. 3rd edition. New York: Springer, 2001.

(3) “Hall Effect Measurements.” National Institute of Standards and Technology Electronics and Electrical Engineering Laboratory Semiconductor Materials Division. 14 August 2007. U.S. Commerce Department. 13 November 2007. <http://www.eeel.nist.gov/812/hall.html>.

(4) E. H. Hall, "On a New Action of the Magnet on Electrical Current," Amer. J. Math. 2, 287-292 (1879).

(5) Ramsden, Edward. Hall-Effect Sensors Theory and Application. 2nd edition. Elsevier, 2006. Online <http://www.knovel.com/knovel2/Toc.jsp?BookID=1653>. Elsevier, 2006. Online <http://www.knovel.com/knovel2/Toc.jsp?BookID=1653>.

(6) “Hall Effect Sensing and Application.” Honeywell, Microsensing and Control. <content.honeywell.com/sensing/prodinfo/solidstate/technical/hallbook.pdf >.

(7) Bridge Technology. <http://www.four-point-probes.com/ecopia.html>.(8) Allegro Microsystems.

<http://www.allegromicro.com/en/Products/Part_Numbers/0754/index.asp>.

(9) Van der Pauw, L.J. Philips Technical Review. Vol. 20 No. 8, 220-224 (1958).� www.magnet.fsu.edu

� people.clarkson.edu/~ekatz/scientists/hall_edwin.html

� hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html#c2


Hall Effect Presentation

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