Springer Handbook of Materials Measurement Methods材料测量测试方法手册

SpringerSpringer HandbookHandbook ofof MaterialsMaterials MeasurementMeasurement MethodsMethods材料测量测试方法手册材料测量测试方法手册 Electrical Properties9 4Semiconductors471 K A 1 C 3 1 Fig 9 5 5Lateral contactof widthw andof lengthd onathin epitaxial layer ofthickness h 9 63 Fig 9 56Equivalent circuitdiagram of a lateralohmiontact aordingto thecurrent distributionin Fig 9 55forthe contact resistance of a metalon athin semiconductorlayertwodifferent terminals needles to measure the result ing small voltage between the contactpads In thisway distorting effectsof additionalcontact resistancesbetween the measurementneedles and the contactpadscan beeliminated A methodfor characterizingcontact resistancesofcontactswithnearlyhomogeneouscurrentflowintove r tical contactsuses contactdots of different diameterson Fig 9 57TLM maskfor thedetermination of the sheetresistance R s and total contact resistance R cfrom whichthe specific contact resistance c can be extracted TLM transmission linemodel the semiconductor to distinguishbetween thespecifiontact resistanceand thespreading resistancecontri butions This methodby Coxand Strackis describedin 9 64 A moreversatile methodwhich ismainly appliedtolateral contactsto thinsemiconductor layerswithstrongly inhomogeneous current flow is thetransmis sionlinemethodbyBerger 9 63 Figure9 55showsthecurrentdistr ibutioninthislateralcontacttype Thesemi conductor layer is assumedwith aspecific resistance s cm anditssheet resistanceR s R s s h Fortechnically relevantcontacts the semiconductorsheetheight his oftenquite lessthan thecontact lengthd For thisconfiguration the followingequivalent circuitcan be derived Fig 9 56 The resistanceof theepi taxiallayeris described by thesum ofits differentialelementsdR1 The specifiontact resistanceR c spec c is rep resented by the distributedvertical elementsdR2 Thetotal contact resistanceR c is the ratioof the voltage attheleft beginningof thecontact regionand thetotalconstant currentI fedinto thestructure Aording tothetransmission linenature ofsuch astructure 9 63 thespecifiontact resistance c maybe extractedfromthe measurement of thetotalcontactresistanceR c Forthat purposedifferentialequationsareformulated 9 63 which can be solvedgiving arelation betweentotal andspecifiontactresistancein animplicit equation 9 66 R c 1w R s c 0 2R sh2 coth R s c 0 2R sh2 d 9 66 This implicitequation allowsthe extractionof c afterRc hasbeen measuredand thegeometrical constantsw h and dof thetest structurehave beendetermined Thesheet resistanceR sof the epitaxial layerbetween twocontactstripes has also to be measuredbefore The measurement of R s and Ran bedone withasetupofthreecontactstripesinaKelvincontactconfig urationwithtwodistancesl1andl2betweentwocontacts Fig 9 57 Twomeasurementsneedtobetaken first thecurrentI mA range is fedthrough theepitaxial layerstripe ofwidthw by using thetwo left hand contacts1 2withdistance l1and measuring thevoltageV1 second thetwo contacts2 3with distancel2are used to measuretherespective voltageV2by drivingthe sameamount ofcurrentthrough theepitaxial layer Part C9 4472Part CMeasurement Methodsfor MaterialsPropertiesFrom thesetwo voltagevalues V1and V2togetherwith theconstant currentI thesheet resistanceR sandthe totalcontactresistanceRcunder eachcontact can becalculated byR s V1 V2l1 l2wI andR c 12 V1I l1R sw 9 67 With thesetwo termsnow 9 66 can beused toextractthe specifiontactresistance c The contactdistancesl1and l2 1 100 m need tobe determinedwith highprecision sub micron range because otherwiselargererrorswouldresultfor c especiallywhen c fallsbelow10 6 cm2 For electricallylong contacts e g d 40 m thetransfer lengthL Tis definedas LT c R s Thetransfer lengthillustrates thetypical lengthfor thecur rent topass from theepitaxiallayer into the metalcontact Practical contactsdo notneed tobe designedlongerthan aboutthree transferlengths Thetransferresistance R T isdefinedasRT Rs c mm Thetransferresistancecharacteri zesthelowestcontact resistancewhich can be achievedfor anelectri callylongcontactofagivenwidthw Transferresistancevalues fore g FETs should be lowerthan0 2 mm 9 5Measurement ofDielectric MaterialsPropertiesDielectricmaterialsarethebuildingblockso ffunctionalelectroniircuits capacitors gatedielectrics tran smis sion linesare essentialas electricalinsulators forpowerdistribution Molecular solids organic polymerresins ceramic glassesand positesof organicresins withceramicfillers representtypical dielectrics The dielec tricpropertiesofmaterialsareusedtodescribeelectricalenergy storage dissipation andenergy transfer Electri calstorageistheresultdielectricpolarization Dielectricpolar ization causescharge displacementor rearrange mentof molecular dipoles Electrical energydissipationor lossresults from 1 electrical chargetransport orconduction 2 dielectric relaxation 3 resonant tran sitionsand 4 nonlineardielectriceffects Energylossiseventually relatedto scattering radiation orconversionof electricalenergy into thermal energy Joule heating Energy transferis relatedto propagationof electro magic waves in dielectricmedia transmission linesandwaveguides where the dielectric permittivitydeter mines thevelocity ofwave propagation attenuation andultimatelythe dimensions of thedevices The mostrelevant physicalprocesses in dielectricmaterials from the practicalviewpoint arethose whichresultin powerloss It isimportant tounderstand thebasiharacteristics of these processesbecause theydetermine the optimalapproach tomeasurement Interaction of electromagic radiation with mater ials at frequencies of about1012Hz and above givesriseto quantizedtransitions between the electronic vibra tional androtational molecularenergy states which canbeobservedbyusingappropriatequantumspectroscopytechnique s Bycontrast thedielectricpropertiesaregov erned byreorientational motionsof molecular dipoles dipolarrelaxation andmotionsofelectricalchargecar riers electrical conduction which leadsto continuousdielectricdispersion and absorption that is observedinthe frequency range of10 6Hz to1012Hz The dielectric relaxation 9 65 describes thedis persion of real permittivity and theourrenceof dielectric absorption Permittivity measurementsallowsfor thedetermination ofmoleculardipolemo ments and subsequently can linkthe relaxationprocesswith moleculardynamics andstructure The dielec tricabsorption loss spectra as a functionfrequencyand temperature 9 66 67 canbeusedtocharac terize moleculardynamics indipolar liquids polarsolvents andsolutes rotator phase crystals nonpo lar andpolar polymers polyethylene polyacrylates epoxy resins polyimides Research on dielectricre laxation inmolecular liquidsand solidswas pioneeredbyFr hlich 9 68 Hill etal 9 69 Bottcher andBordewijk 9 70 and formacromolecules byMc Crum etal 9 71 and Runtand Fitzgerald 9 72 Selected developments indielectricand relatedmo lecular processswere reviewedby Davies 9 73 Since1954 the mostwidely knownand prehen sive workondielectric materials andcorrespondingmeasurements hasbeen thatof vonHippel 9 74 Measurement ofRF propertiesof materialsweresurveyed byBussey 9 75 Broadband waveguidingandfree space measurementmethodologies for theagriculture industrywere developedby Nelsonandco workers 9 76 77 Extensive dielectricdata wereobtainedrecently forferroelectric ceramics bariumPart C9 5Electrical Properties9 5Measurement ofDielectric MaterialsProperties473titanate inorganic andorganic semiconductorsandphotoconductors for ultrathin dielectricsfilms whichhave importantapplications insolid state electroniircuitsand devices Recent advancesin thetheoryof dielectric relaxation and the correspondingexperi mental methodologieswere reviewedby Kremer andSch nhals 9 78 9 5 1Dielectric PermittivityTheinteraction ofelectromagic fieldswith matterisdescribed byMaxwell s equations 9 79 The po larization Pdescribes the dielectric displacementDwhich originates fromtheresponse of the materialtoan externalelectric field EP D 0E r 0 0 E 9 68 where 0is the dielectric permittivity of free space 0 8 854 10 12F m and 0 r i isthe plex permittivity tensor which dependsontemperature frequency and in the caseof anisotropicmaterials on thedirection of the electric field vec tor E The frequencydependence of the permittivityis illustrated in Fig 9 58 Relative permittivity r is adimensionless ratioofplex permittivityto thepermittivityoffreespace 3 0 MM M M 3 0 M Fig 9 58Frequency dependence of thereal r and imag inary rparts of the plex permittivity with a singlerelaxationprocess at the relaxation frequency f r r 0 r i r The dielectric constant is the realpart of therelative permittivity The symbolused inthisdocument is r Other symbolssuch asK k K k rand are symbolsused in the technicalliterature Di electriclosstangenttan isadimensionlessratioofthedielect ric lossto the dielectrionstant tan r r The realpartofdielectric permittivitydecreases by rat acertain frequencyf rwhich givesrise to a corre sponding peakof the dielectric loss r Such frequencydependenceof theplex permittivityindicates adi electric relaxation A dielectricmaterial may exhibitseveral dielectric relaxation processes each associatedwith its characteristic r rand f r dependingon themolecularmechanism involved Thedielectricrelaxationshouldnotbeconfusedwithreso nant transitionsbetween vibrationaland electronicstatesand thosethat originatefrom aresonant behaviorof the electricalmeasurement circuit Dielectric RelaxationUnlikeelectrical conductionin whichcharge carriers electrons ions andholes move physicallythrough thematerial under theinfluence of an electric field thedielectric relaxationoriginatesfromreorientational re sponses ofelectric dipolesto the applied electric field Materials inwhich the dipoles areinduced onlybythe applicationof anelectric fieldare nonpolarmater ials Polar materials on theother hand have permanentmoleculardipoles whichmayexhibita numberofdif ferent relaxationprocesses each havinga characteristicstrengthmeasured by r andacharacteristic relax ation frequencyf r In thesimplest casewith asinglerelaxation time r thedielectricrelaxation function maybedescribedbyDebye s model 9 65 shown by 9 69 Here u isthedielectrionstant athigh frequencies which doesnot containa permanentdipole contribution r u whenf f r Fig 9 58 0 u r1 i r 9 69 Cooperative distortionalpolarization local rotationalpolarizationand interfacialpolarization are the mostmonlyobserved relaxationprocesses In a posite material many orall of these processesmaybe presentand giverise to a veryplex relaxationbehavior which canbe modeledas asuperposition ofseveralrelaxations The Havriliak Negami HN relax ationfunction defined below has oftenbeen foundtoprovide agood phenomenologicaldescription ofdielec tricrelaxationdata inmolecular liquids solidsand glassPart C9 5474Part CMeasurement Methodsfor MaterialsPropertiesformers 9 80 81 0 k u r 1 i r k 1 2 3 9 70 The parameters and describe theextent ofsymmet ric and asymmetric broadening of the plexdielectricfunction where and are 0 1and0f max wavepropagationcauses aspa tial distributionoftheelectricfieldinside thespecimensection which can nolonger betreated asa lumpedcapacitanceand hastobeanalyzed asa microwavework PartC9 5478PartCMeasurement Methodsfor MaterialsPropertiesDielectric MeasurementsUsingMicrowave NetworkAnalysisMicrowave work analyzer terminologydescribesmeasurements ofthe incident reflected and transmittedelectromagicwaves The reflectedwave is measuredat thePort1 andthetransmitted waveismeasuredatPort2 Fig 9 62 Iftheamplitudeandphaseofthe sewavesareknown then itis possibleto quantifythe reflectionand trans mission characteristicsofamaterialundertest MUT withitsdielectricpe rmittivityandthedimensionsofthetest fixture The reflectionand transmissionparameterscanbeexpressedasvector magnitudeandph ase scalar magnitude only or phase only quantities In this no tation impedance andreflectioncoefficientare vectors Network characterizationatlowfrequencies isusuallybased onmeasurementofplex voltageand currentatthe inputoroutputports terminals ofadevice Sinceit isdifficult tomeasure totalcurrent orvoltage athighfrequencies plex scattering parameters S11 S12 S21and S22are generallymeasured instead 9 98 99 Measurements relativetotheincident waveallow tonormalizeand quantifythereflectionand transmissionmeasurementsto obtainvalues thatare independentofboth absolutepowerandvariationsinsourcepowerve r susfrequency Thescatteringparameters S parameters are definedby 9 80 9 99 b1 S11a1 S12a2 b2 S21a1 S22a2 9 80 A generalsignal flowgraph ofa two port workwiththecorrespondingscatteringparameters is showninFig 9 63a Here a1anda2aretheplex ampli tudes ofthe wavesentering thework while b1and 4 4 8 9 K 8 4 9 P8Fig 9 62Block diagramofaworkanalyzer 0 Fig 9 63a d Scatteringparameters signalflow diagrams a two port work b load termination c shunt admit tance d transmission linepartially filledwithadielectricslabb2are plexamplitudes ofthe outgoingwaves Fig ure9 63b showsa terminationor loadhaving reflectioncoefficient Since thereisnotransmitted waveto Port2 b2 0 b1 a1 S11 T