A3-HALLEFFECTLastRevision:August,212007QUESTIONTOBEINVESTIGATEDHowtoindividualchargecarriersbehaveinanexternalmagneticfieldthatisperpendiculartotheirmotion?INTRODUCTIONTheHalleffectisobservedwhenamagneticfieldisappliedatrightanglestoarectangularsampleofmaterialcarryinganelectriccurrent.Avoltageappearsacrossthesamplethatisduetoanelectricfieldthatisatrightanglestoboththecurrentandtheappliedmagneticfield.TheHalleffectcanbeeasilyunderstoodbylookingattheLorentzforceonthecurrentcarryingelectrons.TheorientationofthefieldsandthesampleareshowninFigure1.Anexternalvoltageisappliedtothecrystalandcreatesaninternalelectricfield(Ex).Theelectricfieldthatcausesthecarrierstomovethroughtheconductivesampleiscalledthedriftfieldandisinthex-directioninFigure1.Theresultantdriftcurrent(Jx)flowsinthex-directioninresponsetothedriftfield.Thecarriersmovewithanaveragevelocitygivenbythebalancebetweentheforceacceleratingthechargeandtheviscousfrictionproducedbythecollisions(electricalresistance).ThedriftvelocityappearsinthecrossproducttermoftheLorentzforceasshowninequation1.Thetransverse(y)componentoftheLorentzforcecauseschargedensitiestoaccumulateonthetransversesurfacesofthesample.Therefore,anelectricfieldinthey-directionresultsthatjustbalancestheLorentzforcebecausethereisnocontinuouscurrentinthey-direction(Onlyatransientasthechargedensitiesaccumulateonthesurface).TheequilibriumpotentialdifferencebetweenthetransversesidesofthesampleiscalledtheHallvoltage.AgoodmeasurementoftheHallvoltagerequiresthattherebenocurrentinthey-direction.Thismeansthatthetransversevoltagemustbemeasuredunderaconditiontermed“noload”.Inthelaboratoryyoucanapproximatethe“noload”conditionbyusingaveryhighinputresistancevoltmeter.THEORYThevectorLorentzforceisgivenby:(1)whereFistheforceonthecarriersofcurrent,qisthechargeofthecurrentcarriers,Eistheelectricfieldactingonthecarriers,andBisthemagneticfieldinsidethesample.Thechargemaybepositiveornegativedependingonthematerial(conductionviaelectronsor“holes”).Theap