questions and answers regarding resistivity, resistance, surface resistivity, sheet resistance and...

Upload: siladittya-manna

Post on 10-Mar-2016

13 views

Category:

Documents


0 download

DESCRIPTION

Qs

TRANSCRIPT

  • 7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity

    http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 1/6

    QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivitybyJohnClark,C.Eng,M.I.Mech.E.,F.B.H.I.,ManagingDirectorofJandelEngineeringLtd.

    Thefollowingcommentsarebasedonelementaryphysics(beforesemiconductors!)andsomeyearsmeasuringsemiconductorsandthinfilms.Theyaremyopiniononly,butdontgetcriticizedinpractice!

    ***

    Q.Iwouldliketoknowwhyusingafourpointprobeyoudonthavetroublewithcontactresistancesusingtwocurrentinjectionprobesandtwovoltageprobes,thevoltageprobesstillprobethevoltagethroughaSchottkybarrier(formetalprobesonansemiconductor),sotheystillseethevoltagedropthroughthisbarrier.So,couldyoutellmewhereIamwrong?

    A.Theveryreasonforfourpointprobemeasurementsistodivorcetheprobessupplyingthecurrentfromtheprobesmeasuringthevoltage,soitisonlynecessarytoconsiderthevoltageprobes.Thedeviceusedtomeasurethevoltageisprovidedwithaveryhighinputimpedance(ASTMF84recommendsatleast10^6xtheresistivityofthespecimen),thusthecontactresistanceisasmallproportionoftheresistanceinthevoltagemeasuringcircuit.Compoundsemiconductorshaverelativelylargecontactresistance,andunlessheavilydopedarenotmeasurablewithanormalDC4pointprobemeasuringsystem.Thepressureofthe4pointprobeneedlesinvariablydamagesthecrystalstructurebeneaththeneedles.Wesupposethatsuchdamagepromotesohmiccontactbylargelyeliminatingtherectifyingdiodesyoumentioned.

    ***

    Q.Isthereadifferencebetweensheetresistanceandsheetresistivity?Atleastoneauthorclaimsthereis.

    A.Thisisloosethinking.Sheetresistanceismeasuredinohmspersquare

    TECHNICALINFORMATION

    1ShortApplicationNoteonSheetResistance,OhmsPerSquare,andtheCalculationofResistivityorThickness2Basicinformationregarding

    howtomakefourpointprobemeasurementsusingJandelresistivitytestequipment.3FourPointProbeTheoryA

    helpfularticle4FourPointProbeEquationsA

    helpfularticlefromtheUniversityofIllinoisUrbana/Champaign5Understandingvolume

    resistivitymeasurementsandconvertingbetweenohmspersquare(sheetresistance)andohmscm(volumeresistivity)6SampleSizeRequirementsand

    CorrectionFactorsSomequestionsandanswersfromJandelEngineeringLtd.7HaldorTopsoeTechnical

    DocumentsRegardingCorrectionFactorsCorrectionFactorforvariousmaterialshapesandsizes81964NationalBureauof

    StandardsTechnicalNote199,"CorrectionFactorTablesforFourPointProbeResistivityMeasurementsonThin,CircularSemiconductorSamples"9FiniteSizeCorrectionsfor4

    PointProbeMeasurements,byJ.R.Senna,InstitutoNacionaldePesquisasEspaciais(INPE),Brasil10Questionsandanswersre:

    resistivity&resistance,sheetresistance,volumeresistivity,surfaceresistivitybyJohnClarkofJandelEngineering

    HOME PRODUCTS TECHINFO FAQ CONTACT

  • 7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity

    http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 2/6

    whileanykindofresistivityismeasuredinohms.cmorohm.metre.Ibelievethetwoexpressionsaresynonymous.

    ***

    Q.Issheetresistance/resistivityaninherentpropertyofamaterial,orisitafunctionofthickness?

    A.RESISTIVITYistheinherentpropertyofthematerialwhichgivesitelectricalresistance.ItissometimescalledSpecificResistance.Sheetresistanceistheresistanceofathinsheetofmaterialwhichwhenmultipliedbythethickness(incm)givesthevalueofresistivity.

    ***

    Q.Atleastoneauthorclaimsthatsurfaceresistivityisamoreprecisemeasurementwhendealingwithinsulatingorslightlyconductivematerialstheproblemwithevaluatingsurfaceresistivityinhighlyconductivematerialsistheunderlyingassumptionthatelectronsmovefromthenegativeelectrodeacrossthetopsurfaceoftheconductivelayeronlytothepositivelayer.Inotherwords,heseemstobeimplyingthatyoucantmeasuresurfaceresistivityonhighlyconductivematerials.True?

    A.True.

    ***

    Q.Anotherauthorseemstobackup#3:Exceptintheory,thereisnosuchthingassurfaceresistivity.Physicshandbookslistsurfaceresistivityvaluesfordielectrics(novaluesbelow108W/square),butnosurfaceresistivityvaluesarelistedforconductivematerials.Volumeresistivityvaluesaregivenforbothinsulatorsandconductors.Insulatorshaveverythin(i.e.,severalmolecularlayersthick)conductivesurfacesbutthesurfaceconductivityofaconductorssurfaceisindistinguishablefromitsvolumeconductivity.Onaninsulativesubstratesuchassapphire,athinconductiveconductivefilmhasasurfaceresistivityrelatedtoitsthickness.Generally,oneshouldnotassumethatsurfaceandvolumeresistivitiesarerelated.Ifindthisveryinteresting.Hesbasicallysayingthataninsulatorreallyhasathinconductivelayer,andthatitispossibletomeasureitsresistivity,butitisnotpossibletomeasuresurfaceresistivityofaconductor.

    A.SurfaceresistivitythisisadifferentanimalwhichIamnotclearabout.AsfarasIknowitcantbemeasuredwithafourpointprobe.Itseemstobedonewithconductiveelectrodespressedontothespecimenandahighvoltageappliedwhenthecurrentwhichflowsismeasured.IbelieveASTMD99189orIEC93areapplicable.ItusuallyseemsrelatedtoinsulatorsandIhavenoexperienceofthiskindofmeasurement.AccordingtomybookofTablesofPhysicalandChemicalConstants(KayeandLaby)SurfaceResistivityisdefinedastheresistancebetweenoppositeedgesofasquare,andtheunitistheohm(persquare).Thetablesgiveafigureforvariousmaterialsafteraperiodofoneminuteofapplicationofthemeasurementvoltage.Thisisbecausetheinsulatorbecomescharged.

    11Q&Aregardingtheuseof

    JandelResistivityMeasurementequipmentbyPeteClarkofJandelEngineering12FourPointProbeTheoryof

    OperationfromtheUniversityofCalifornia,Berkeley,EECSwebsite(PDFfile)13Atableofsuggestedprobetip

    specificationsforvarioussiliconwafertypes.14Atableofcommonfourpoint

    probetipradiiandspacings15Osmiumalloytipsversus

    tungstencarbidetips16Squarearrayversuslinear

    arrayfourpointprobe17Reversingcurrenttocheckthe

    validityofa4pointprobemeasurement18Determiningthebestchoiceof

    probetipspecifications(tipspacing,springloads,material,radii)foragivenmaterial.19Whatistheexpectedlifeofa

    JandelFourPointProbeHead?20JandelFAQ

    HallEffectMeasurementTechnicalinfo:21Wikipediaarticleregardingthe

    HallEffect22Wikipediaarticleregardingthe

    VanderPauwmethod23NISTwebpageregardingthe

    theoryandimplementationoftheHallEffectMeasurementtechnique

  • 7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity

    http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 3/6

    ***

    Q.Youseemtobestatingthatthereisadifferencebetweensheetresistanceandsurfaceresistance.Iwasntawareofthis,whichisprobablywhyIvebeensoconfused!Soisittruethereisadistinctionbetweenthetwo?

    A.IthinkthatsurfaceresistancerelatesprincipallytoinsulatorsasIremarkedpreviously.IhavesomemoreinformationfromKeithleyInstrumentsseetheirapplicationnote#314(volume_surface.pdf)483KPFDfilewhichrefersadditionallytoASTMD257.Pleasenote:Agilentoffersasystemaswell,the4339B.Welistthesehereforyourconvenience,however,BridgeTechnologydoesnotofferequipmentformeasuringnearinsulatorswhicharemeasuredassurfaceresistivity.Weofferequipmentforthewellestablishedfourpointprobemeasurementwhichisformeasuringsemiconductors,metals,oxides,etc.,andwhichprovidessheetresistancevalues(formeasuringthinfilms)expressedinohmpersquare,andvolume(orbulk)resistivityvaluesexpressedinohmscm.Surfaceresistivityinstrumentsmeasureresistivitiesintherangefrom10^9to10^16ohmspersquareandareoftenusedtomeasurematerialssuchasESDpackagingmaterials,bags,etc.Someofthesesystemswillhavecontactsonthetopandbottomofthesubstratewhileotherswillhaveeitheracontactingringwithoneprobeinthecenter,orthreeprobesinatrianglearrangementwithafourthprobeinthecenter.Theprobesaresometimesmadeofconductiverubber.Moreinformationaboutsurfaceresistivitymeasurementsisavailablehere:ohmspersquarewhat.pdf

    ***

    Q.LetssayIhaveasamplethatsinfinitein3dimensions,andIusea4pointprobemeasuresresistance.Willtheresistancebeindependentofprobespacing?Theequationsseemtoimplythis.

    A.Suchasampleisusuallydefinedasasemiinfinitevolumeifitextendstoinfinityinalldirectionsbelowaplaneonwhichfourprobesarelocated.Forequidistantprobes:Resistivity=2xpixsx(V/I)wheresistheprobespacingincm.

    ComparethiswithathinsamplewhenResistivity(rho)=pi/(logn2)xV/Ixtwheretisthethicknessandpi/(logn2)xV/Iisthesheetresistance.Henceitcanbeseenthattheformulaisindependentofspacing.

    ***

    Q.Asyoustated,theequationforvolumeresistivityofasemiinfinitevolumeis:

    Resistivity=2xpixsx(V/I)

  • 7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity

    http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 4/6

    wheresisthe(equidistant)probespacingincm.

    Forahomogenousmaterial,theresistivityisconstant,correct?Thusnomatterwhattheprobespacingis,andnomatterwhatthemeasuredresistancevalueis(V/I),theresistivityvalueshouldalwaysbethesame,correct?

    Rearrangingtheequation,youhave:

    resistivity/(2*pi)=s*(V/I)

    Thelefthandportionshouldbeconstantforahomogenousmaterial,regardlessofsorresistancevalue.

    Thisimpliestheprobespacingandtheresistance(V/I)areinverselyproportionalifsisdecreased,themeasuredresistance(V/I)mustincrease,andifsisincreased,themeasuredresistance(V/I)mustdecrease.Isthiscorrect?Butitwouldseemasifthe*opposite*wouldhappen,i.e.assisincreased,theresistance(V/I)wouldincrease.

    A.YourargumentaboutsandV/Imustbevalid.Althoughonemightsupposethatalargerspacingonthesamplemightresultinalargervoltagedrop,inpracticeitdoesntworkthatway.

    ***

    Q.Doyouhaveanypapersthatexplainallofthis?

    A.TheearliestpaperisbyLBValdesProcIREFeb1954ResistivityMeasurementsonGermaniumforTransistorspages420427.

    Thereareahostofothers,principallyconcernedwithcorrectionfactorsforspecialcases.

    a)LinearArrayProbes

    Circularwafersatcentre:

    1. 1.D.E.Vaughan,Br.J.Appl.Phys.,12,414(1961)

    2. M.A.Logan,BellSys.Tech.J.,40,885(1961)Offcentrebutonradius:

    3. L.J.Swartzendruber,NationalBureauofStandardsTechnicalNote199(1964)Perpendiculartoradius:

    4. M.P.AlbertandJ.F.Combs,IEEETrans.ElectronDevices,ED11,148(1964)

    5. L.J.Swartzendruber,SolidStateElectronics,7,413(1964)Rectangularsampleatcentreandoffcentre:

    6. M.A.Logan,BellSys.Tech.J.,46,2277(1967)Halfcylinder:

    7. E.B.Hansen,Appl.Sci.Res.,8B,93(1960)Circularrod:

    8. H.H.Gegenwarth,SolidStateElectronics,11,787(1968)

  • 7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity

    http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 5/6

    Rectangularbar:

    9. A.MarcusandJ.J.Oberly,IEEETrans.Electron.Devices,ED3,161(1956)

    Note:Alltheforegoingisbasedonmeasurementusingafourpointlinearprobe,thecurrentbeingpassedbetweentheouterprobesandthevoltagemeasuredacrosstheinnertwoprobes.

    b)SquareArrayProbes

    Smallsliceatcentre:as9aboveSmallslicealongaradius:as3aboveSquaresample:10.M.G.Buehler,SolidStateElectronics,10,801(1967)Thicksamplenearboundary:11.S.B.Catalano,IEEETrans.Electron.Devices,ED10,185(1963)thininfinitesheet:as10above

    Note:Squarearrayprobeshavethecurrentpassedbetweentwoadjacentprobesandthevoltagemeasuredacrossthetwooppositewhenusedforresistivitymeasurement.

    writtenbyJohnClark

    JandelEngineeringLimitedGrandUnionHouseLeightonRoadLinsladeLeightonBuzzardBedfordshireLU71LAUnitedKingdom

    Phone:+441525378554Fax:+441525381945Email:[email protected]:www.jandel.co.uk

    RegisteredinLondonNo.917424

    FourPointProbesisadivisionofBridgeTechnology.TorequestfurtherinformationpleasecallBridgeTechnologyat(480)9882256orsendemailtoLarryBridgeat:[email protected]

    Torequestfurtherinformationortoplaceanorder,pleasecontactLarry

    BridgeatBridgeTechnologyintheUSAat:(Voice)4809882256,Email:

    [email protected]:4804520172

    HOME|PRODUCTS|TECHINFO|FAQ|ABOUT|CONTACT

    COPYRIGHT2013FOURPOINTPROBES.POWEREDBYBRIDGE

    TECHNOLOGY.

  • 7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity

    http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 6/6