questions and answers regarding resistivity, resistance, surface resistivity, sheet resistance and...
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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!
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Q.Iwouldliketoknowwhyusingafourpointprobeyoudonthavetroublewithcontactresistancesusingtwocurrentinjectionprobesandtwovoltageprobes,thevoltageprobesstillprobethevoltagethroughaSchottkybarrier(formetalprobesonansemiconductor),sotheystillseethevoltagedropthroughthisbarrier.So,couldyoutellmewhereIamwrong?
A.Theveryreasonforfourpointprobemeasurementsistodivorcetheprobessupplyingthecurrentfromtheprobesmeasuringthevoltage,soitisonlynecessarytoconsiderthevoltageprobes.Thedeviceusedtomeasurethevoltageisprovidedwithaveryhighinputimpedance(ASTMF84recommendsatleast10^6xtheresistivityofthespecimen),thusthecontactresistanceisasmallproportionoftheresistanceinthevoltagemeasuringcircuit.Compoundsemiconductorshaverelativelylargecontactresistance,andunlessheavilydopedarenotmeasurablewithanormalDC4pointprobemeasuringsystem.Thepressureofthe4pointprobeneedlesinvariablydamagesthecrystalstructurebeneaththeneedles.Wesupposethatsuchdamagepromotesohmiccontactbylargelyeliminatingtherectifyingdiodesyoumentioned.
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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
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7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity
http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 2/6
whileanykindofresistivityismeasuredinohms.cmorohm.metre.Ibelievethetwoexpressionsaresynonymous.
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Q.Issheetresistance/resistivityaninherentpropertyofamaterial,orisitafunctionofthickness?
A.RESISTIVITYistheinherentpropertyofthematerialwhichgivesitelectricalresistance.ItissometimescalledSpecificResistance.Sheetresistanceistheresistanceofathinsheetofmaterialwhichwhenmultipliedbythethickness(incm)givesthevalueofresistivity.
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Q.Atleastoneauthorclaimsthatsurfaceresistivityisamoreprecisemeasurementwhendealingwithinsulatingorslightlyconductivematerialstheproblemwithevaluatingsurfaceresistivityinhighlyconductivematerialsistheunderlyingassumptionthatelectronsmovefromthenegativeelectrodeacrossthetopsurfaceoftheconductivelayeronlytothepositivelayer.Inotherwords,heseemstobeimplyingthatyoucantmeasuresurfaceresistivityonhighlyconductivematerials.True?
A.True.
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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
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7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity
http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 3/6
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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
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Q.LetssayIhaveasamplethatsinfinitein3dimensions,andIusea4pointprobemeasuresresistance.Willtheresistancebeindependentofprobespacing?Theequationsseemtoimplythis.
A.Suchasampleisusuallydefinedasasemiinfinitevolumeifitextendstoinfinityinalldirectionsbelowaplaneonwhichfourprobesarelocated.Forequidistantprobes:Resistivity=2xpixsx(V/I)wheresistheprobespacingincm.
ComparethiswithathinsamplewhenResistivity(rho)=pi/(logn2)xV/Ixtwheretisthethicknessandpi/(logn2)xV/Iisthesheetresistance.Henceitcanbeseenthattheformulaisindependentofspacing.
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Q.Asyoustated,theequationforvolumeresistivityofasemiinfinitevolumeis:
Resistivity=2xpixsx(V/I)
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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.
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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)
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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
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7/19/2015 QuestionsandAnswersRegardingResistivity,Resistance,SurfaceResistivity,SheetResistanceandVolumeResistivity
http://fourpointprobes.com/questionsandanswersregardingresistivityresistancesurfaceresistivitysheetresistanceandvolumeresistivity/ 6/6