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MicrowaveWireless Communications FromTransistorto SystemLevel

UniversityofFerrara,Ferrara,Italy

UniversityofMessina,Messina,Italy

AntonioRaffo

GiovanniCrupi

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Notices

Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchand experiencebroadenourunderstanding,changesinresearchmethods,professional practices,ormedicaltreatmentmaybecomenecessary.

Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledge inevaluatingandusinganyinformation,methods,compounds,orexperimentsdescribed herein.Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyand thesafetyofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility.

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PrintedintheUnitedStates

AdAlessandro,l’Amoredipapà AntonioRaffo

AimieicarigenitoriCarmeloeTeresa AimieifratelliVincenzo,Felice,IsodianaeGiuseppe EdamiamoglieGabriella

GiovanniCrupi

Contributors

G.Avolio

KULeuven,Leuven,Belgium

K.Burger

Qualcomm,SanDiego,CA,UnitedStates

A.Caddemi

UniversityofMessina,Messina,Italy

V.Camarchia

PolitecnicodiTorino,Torino,Italy

W.Chen

TsinghuaUniversity,Beijing,China

X.Chen

TsinghuaUniversity,Beijing,China

E.Cipriani

UniversityofRomeTorVergata,Rome,Italy

P.Colantonio

UniversityofRomeTorVergata,Rome,Italy

G.Crupi

UniversityofMessina,Messina,Italy

S.Farsi

KULeuven,Leuven,Belgium;QualcommInc.,SanDiego,CA,UnitedStates

A.Ferrero

KeysightTechnologies,SantaRosa,CA,UnitedStates

F.Giannini

UniversityofRomeTorVergata,Rome,Italy

E.McCune

RFCommunicationsConsulting,SantaClara,CA,UnitedStates

B.Moser

Qorvo,Inc,Greensboro,NC,UnitedStates

M.Pirola

PolitecnicodiTorino,Torino,Italy

A.Raffo

UniversityofFerrara,Ferrara,Italy

F.Ramirez

UniversityofCantabria,Santander,Spain

S.Sancho

UniversityofCantabria,Santander,Spain

D.M.M.-P.Schreurs

KULeuven,Leuven,Belgium

A.Suarez

UniversityofCantabria,Santander,Spain

G.Vannini

UniversityofFerrara,Ferrara,Italy

Z.Wang

MicrosoftCorp.,Beijing,China

P.J.Zampardi

Qorvo,Inc,NewburyPark,CA,UnitedStates

S.Zhang

SmarterMicroInc.,Shanghai,China

AbouttheEditors

AntonioRaffo isaresearchassociateattheUniversityofFerrara,Italy,wherehe teachescoursesinsemiconductordevicesandelectronicinstrumentationandmeasurement.Hisresearchactivityismainlyorientedtononlinearelectrondevicecharacterizationandmodelingandcircuit-designtechniquesfornonlinearmicrowave andmillimeter-waveapplications.Antoniohascoauthoredover100publications ininternationaljournalsandconferences.HeisamemberoftheTechnicalProgrammeCommitteeoftheIEEEINMMiCconferenceandservesasanassociateeditor ofInternationalJournalofNumericalModelling:ElectronicNetworks,Devices andFields.AntonioisamemberoftheIEEEMicrowaveMeasurementTechnical Committee(MTT-11).

GiovanniCrupi isatenuretrackassistantprofessorattheUniversityofMessina, Italy,whereheteachesmicrowaveelectronics,laboratoryofwirelesstechnologies, bioengineering,andoptoelectronics.Since2005,hehasbeenarepeatvisiting scientistwithKULeuvenandIMEC,Leuven,Belgium.Giovanni’smainresearch interestsincludesmallandlargesignalmodelingofadvancedmicrowavedevices. HeisamemberoftheTechnicalProgrammeCommitteeoftheIEEEINMMiC andTELSIKSconferencesandservesasanassociateeditorof InternationalJournal ofNumericalModelling:ElectronicNetworks,DevicesandFields.Giovanniisthe chairoftheIEEEMicrowaveTheoryandTechniquesSociety(MTT-S)Fellowship program.

ForewordbyCharlesF.Campbell

Mobilecommunicationsandconnectivityhavedrivenamultitudeofadvancements inRFandmicrowavesemiconductorandcircuittechnology.Whiletheseadvancementshaveenabledthemobilecommunicationrevolution,theyalsopresentcircuit andsystemdesignerswithmanydifferentoptionsandapproachesforproductrealization.ThedaysarelonggonewhendesignerssimplyoptimizedaGalliumArsenideintegratedcircuitforsaturatedoutputpowerandefficiency.Today’scircuitand systemsengineersmustbefarmoreknowledgeableintheoverallproductdevelopmentprocess.Proficiencyindevicephysics,modelingandcharacterization,circuit design,architectureandapplication,signalmodulationformats,measurements,and industrystandardsareallrequiredtosuccessfullydesignmodernreceiveandtransmitcomponents.Manyengineeringanddesigndecisionsmustbeconsideredtobalancecost,performance,andcycletimewhilesimultaneouslymeetingchallenging productspecifications.Specificexampleswouldbeselectinganoptimumsemiconductortechnology,devicecharacterizationandmodeling,circuitarchitecture,linearizationstrategy,andoverallsystem-levelconsiderations.Althoughtherearemany excellentbooksandarticlesthatcoverthesetopicsindepth,itisfarmoredifficultto findacomprehensivesourceofinformation.Inthisbook,“MicrowaveWireless Communications:FromTransistortoSystemLevel,”ateamofwell-knownindustry andacademicexpertshasbeenassembledtoprovideathoroughtreatmentofthese topics.Theauthorsdonotsimplyrepeatstandardexplanationsofthesesubjects,but presentuniqueapproaches,perspectives,andalternatepointsofviewthatgreatly enhanceone’sunderstandingofthesecomplexideas.

Thisbookbeginswithanintroductiontotransistormodelingandextraction, highlightingdevicecharacteristicsandbehavior.Sectionsonlinear,nonlinear,and noisemodelingareincludedalongwithmodelingresultsofactualdevices.

Chapter2 focusesontestandmeasurementsystemsfordevicecharacterization, includingdiscussionsofnonlinearvectornetworkanalyzersandactiveload pull.Blockdiagramsofthesemeasurementinstrumentsareprovidedandexplained indetail.

Chapter3 isthestartofthecircuitdesignportionofthebook,presentingacomprehensivediscussionofoscillators.Thishighlytheoreticaldiscussionisintroduced bywayofsimpleidealizedoscillatorcircuits—tobringthereaderuptospeedwith basicprinciples.Thisisfollowedbyamorerigorousanalysis,applicabletoreal oscillators,alongwithdesignexamplesusingacommerciallyavailabledevice.

Chapter4 coversthetopicofpoweramplifiers,andstartswithparameterdefinitions andfiguresofmerit.Thisisfollowedbyanintuitivediscussionofloadlineanalysis andpoweramplifiermodesoperation.Circuitarchitectures,implementation,and amplifierlinearityarealsodescribedinthissection.

For Chapter5,thebookreviewshowsystem-levelconstraintsimpactcircuit designdecisions.Aspectssuchasbatterylife,probabilityfunctionsfortransmit power,amplifierlinearizationtechniques,andpoweramplifiermodulearchitectures

arediscussedatahighlevel.Thisisfollowedbyadiscussionofavailabledevices, passivesandboardtechnologies,andhoweachrelatestoperformance,costand schedule. Chapter6 coverspoweramplifierdesign,includingarchitectureandlinearizationtechniques.TheDohertyamplifierconceptisthoroughlyreviewedaswell asbroadbandanddigitalimplementations.Thisisfollowedbyapresentationofpopularlinearizationapproaches,includingenvelopemethods(envelopetracking(ET) andenvelopeeliminationandrestoration(EER))andlinearamplificationwithnonlinearcomponents(LINC)approaches(Chireix,multilevelandmode-multiplexing).

Thefinaltwochaptersfocusontheanalysisofpoweramplifierlinearizationand efficiencyenhancementmethods.Theauthorof Chapter7 takesaninteresting approachtoinvestigatingtheeffectivenessofefficiencyenhancementmethods. Usingtransistorpowercompressioncurves,threeoperationalmodesaredefined (L,P,andCmodes)basedonthehowdeepthedeviceisingaincompression.Simple circuitmodelsforeachmodearedevelopedwhich,alongwiththetransistorIVcurves,areusedtoanalyzeoutputpowerandefficiencyofadevicesubjectedto envelopetrackingandpolarmodulation. Chapter8 coverstechniquesforthecharacterizationandanalysisofnonlinearcircuits.Nonlinearcircuittransferfunctions andVolterraseriesarereviewed,includingsystemswithandwithoutmemory.Then, standard2-tonecharacterizationtechniquesareexpandedtomoresophisticatedmultisineandoffsetmultisineapproaches.Theresultsareappliedtotheanalysisand modelingofanactualpoweramplifiertoillustratevariousnonlineareffects.

HopefullyIhavesuccessfullyhighlightedthecontentofthisbookandconvinced youtoexamineitpersonally.Practicingmobilecommunicationengineers,aswellas thosewhosimplyseekabetterunderstandingofthiscomplexsubject,willbenefit fromthecontentofthiswork.Theauthorsandeditorsshouldbecongratulatedfor sharingtheirknowledgeandperspectiveofthistopicwiththeengineering community.

CharlesF.Campbell,Ph.D. Qorvo,Richardson,Texas,UnitedStates

ForewordbyRameshK.Gupta

Systemsengineeringenablestherealizationofcomplexsystemfunctionsthrough carefulchoice,andacombinationofinteractingsystemelementsassembledto achievespecificanddefinedobjectives.RFandmicrowavesystemsaredesigned forapplicationssuchasradioastronomyandspaceexploration,navigation,radars, wirelessterrestrialandsatellitecommunications,remotesensing,RFidentification, electronicwarfare,medicalimaging,monitoringandsensing,automotivecollision avoidancesystems,etc.Typically,theseRFsystemsareintegratedwithvarioussubsystemsandelements,suchaslow-noiseamplifiersandfrontends,frequency sources,frequencyconverters,intermediateandhighpoweramplifierswithtransmit and/orreceiveantennas,andradiatingelements.RealizationoftheseRFsubsystems oftenrequireshighfrequencyRFtransistorsanddevicesthatareembeddedand assembledwithpassivecircuitsofmicrostriplinesprintedonasubstrate,and/or coaxialorwaveguideelements,usedinthedesignandparticularwirelesscommunicationapplication.

EffectiveRFandmicrowavesystemsengineeringrequiresanin-depthunderstandingofinteractionsbetweendevices,circuits,andsystemsfordeveloping solutionsthatcanbemanufacturedcost-effectively,andwithrequiredperformance, repeatability,andreliability.Thisisparticularlyimportantforhighvolumedeploymentandproductionofwirelesssystemsanduserequipment,includinghand-held andwearabledevices(eg,smartphones,tablets,smartwatches,etc.)whereconsumersdemandthehighestperformance,functionality,andrepeatableperformance atthelowestpossibleprice.Ithasbeenachallengeforpracticingwirelesscircuit, devicedesign,andsystemengineerstofindtherequisiteinformationfortheirdesign anddevelopmentefforts.Therefore,IbelievethatDr.AntonioRaffoandDr.GiovanniCrupi,theeditorsofthebook“MicrowaveWirelessCommunications:From TransistortoSystemLevel ,”havedoneagreatservicetothemicrowaveandRFcommunitybyputtingtogetherimportantandrelevantinformationonsystems,circuits, anddevicesinasinglevolumewithcontributionsfromauthorsthathaveextensive researchexperienceandexpertiseinthespecifictechnicalareasandtopicsincluded ineachoftheeightchapters.

Goingthroughthetableofcontentsforthisbooksentmeonanostalgicjourney throughmyowncareer,whichspannedworkinRFdeviceandcircuitmodeling, satelliteandwirelesssubsystemdevelopmentandsystemdesign,andmodeling, aswellasthedeploymentandoperationsofthesesystemsanddevices.Istarted mycareerwiththeinvestigationoftwo-terminalsolid-statedevices,suchasGunn andIMPATTdiodes,forsystemapplications.TheissuesofRFparameterdeembedding,linearandnonlinearcircuitanalysisandmodeling,aswellastheirnoise behavior,wererelevantthenfortheirsysteminsertion.Thetwo-terminalRFdevices werequiteconstrainedbecauseoftheir“noisybehavior”andsignaldistortioncharacteristicsduringlargesignalconditions.Emergenceofthree-terminalGallium Arsenidemetal-semiconductorfield-effecttransistors(MESFETs)andthemany

derivatives—includinghighelectronmobilitytransistors(HEMTs)andpseudomorphicHEMTs(p-HEMTs),etc.—andtheirintegrationontomonolithicmicrowave integratedcircuits(MMICs)onGaAssubstrates,aswellasdevelopmentofsilicon basedRFintegratedcircuits(RFICs),havehadarevolutionaryimpactontheminiaturizationofRFsystems.SomeexamplesofthesesystemsincludethehighperformanceradarsusingT/Rmodules,satellitesystemswithflexibleandsteerablebeams, andwirelesssystemswithsmallersize,broaderbandwidth,andrepeatableperformancewithhigherreliability.Byeffectivesystemdesign,thesesystemscanbemanufacturedanddeployedatasignificantlyreducedcost.DuringmyworkatCOMSAT Laboratories,usingthedevice,circuit,system,measurement,andcalibrationtechniquessimilartoonesdocumentedinallthechaptersofthisbook,wewereable todevelopminiaturizedreceivers,poweramplifiersandtransmitters,frequencyconverters,andswitchmatricesfordynamicsatellitebeamswitching.Wealsosuccessfullydevelopedproof-of-conceptC-,X-,andKu-bandphasedarrayantennasfor satellitebeamshapingandsteeringforon-boardandgroundsatelliteapplications. Itisgratifyingtoseemanyofthesesubsystemsandsystemsandtheirderivatives nowbeingcomponentsofthemajorityofmodernsatelliteandwirelessnetwork architectures.

GiventhestateoftheRFandmicrowavetechnologytoday,Iremainveryenthusiasticonemergenceofnewinnovativewirelesssystems.Duringthecomingyears anddecades,manynewapplicationsarelikelytobecomeavailable,includingwearablehealthcaredatasensingandmonitoringsystems,self-energizingimplantable medicalsystems,autonomousandinterconnectedvehicles,collisionavoidancesystems,nondestructivemedicalimagingusingterahertz(THz)frequencies,contactless paymentsystems,etc.Itismyhopethatstudents,engineers,andresearchers involvedinRFandmicrowavepracticewillbeabletoenhancetheirunderstanding ofdevice,circuit,andsysteminteractionsthroughconceptsandtechniquespresented inthisbook,andhelpcreateexcitingsystemapplicationsandsolutionsforthebenefit ofmankind.

Preface

Thewirelesscommunicationmarkethaswitnessedtremendousgrowthinrecent years.Totheconsumer,thisgrowthmanifestsitselfviatheproliferationofmobile telephones,tablets,gamingconsoles,andsoon,theInternetofThings.Thedesignof thesewirelesscommunicationsystemsrequiresin-depthunderstandingoftheir microwavefunctionality,startingfromthetheoreticalunderpinningsoftheirinner workingstotheirpracticalsystem-leveldeployment.

Thedesignofmicrowavewirelesssystemstraversesthreedifferentstages,oftentimesdubbedthedevice,circuit,andsystemlevels.Inspiteofthevastarchivalliteraturedealingwitheachofthesedesignlevels,thusfarnobookhasdetailedthe linksandinteractionsamongthem.Notsurprisingly,microwaveengineersoften acquiredeepexpertiseinonelevel,butlackunderstandingofotherlevels,especially theirinteractions,whichcomplicatesthecollaborationandprojecthandoverbetween designteams,andstiflesinnovation.Asanexample,engineersworkingondevice modelingoftentimesexperiencedifficultiesunderstandingthedifferentoperating modesoftransmittersbasedondynamicpowersupplypoweramplifiers(DPSPA),despitethefactthatDPS-PAoperatingmodesareinherentlyandsimplyrelated totransistoroperation.

Thegoalofthisbookistoelucidatelinksbetweenthedifferentlevelsinmicrowavewirelesssystemdesignbydescribingandunravelingtheirinteractions.The book’smultipleexpertauthorsofferdistinctandcomplementaryviewpointsof thesubjectmaterial.Together,theirtwoforewordsandeightchaptersprovidecomprehensivecoverageofthevasttopicarea.Whileindividualcontributionsfocusprimarilyononeofthethreedifferentdesignlevels,altogethertheyalsotouchon interactionsbetweenlevels,andaddressthepresentlysiloedknowledgeofthesubjectfield.Forexample,thereaderwilllearnthatdesignlinksbetweenthedevice andthecircuitlevelsarenotsodifferentwhendealingwithamplifiers,mixers,or oscillators,andthatlimitationsarisingfromtransistorlinearandnonlinearparasitic elementsarelargelythesame,eventhoughtheyimpactdifferentquantities(noise, poweraddedefficiency,conversiongain,resonanceconditions).

Wehopethisbookwillbecomeavaluedresource,notonlyforresearchers,engineers,andteacherswishingtoextendtheirknowledgeofmicrowavewireless systemsbeyondthepresentlystratifiedliterature,buttoallthoseseekingabetter understandingofthelinkagesanddependenciesbetweendifferentdesignlevels.

Weverymuchhopethatthereaderwillenjoyherorhisjourneythroughthethree differentlevelsofthemicrowavewirelesssystemdesign!

AntonioRaffoandGiovanniCrupi

Microwavetransistor modeling 1

G.Crupi*,A.Raffo†,G.Avolio{,A.Caddemi*,D.M.M.-P.Schreurs{ andG.Vannini†

UniversityofMessina,Messina,Italy* UniversityofFerrara,Ferrara,Italy† KULeuven,Leuven,Belgium{

CHAPTEROUTLINE

1.1 INTRODUCTION

Microwavetransistormodelingisanevergreenresearchfieldofparamountimportance.Thesignificantinterestaroundthistopiccomesfromthefactthatthetransistor isthekeycomponentinhigh-frequencycircuitsthatareattheheartofmodernwirelesscommunicationsystems,suchasmobiletelephony.Tomeetthemoreandmore stringentrequirementsofwirelesscommunicationsystems,transistortechnologies areincessantlyprogressing.Hence,theneedforexploitingemergingtechnologies attheirbestmakesmicrowavetransistormodelinganopenresearchfieldincontinuousevolution.

Thisfirstchapterismeanttogiveacomprehensiveoverviewofthefundamentals, state-of-the-art,challenges,andfuturetrendsinthefieldofmicrowavetransistor modeling,goingfromlinear(alsonoise)tononlinearoperation.

Thechapterisstructuredintosixmainsections,includingthisintroduction.The nextsectionisdevotedtothemicrowavetransistortechnologies.Ofthevarious microwavetransistors,theanalysisofthepresentchapterisfocusedonthehighelectron-mobilitytransistor(HEMT).Hence,thephysicalstructureandtheoperation principlesofthismicrowaveactivesolidstatedeviceareconciselyreviewed.

Inparticular,transistorsfabricatedusingbothgallium-arsenideandgallium-nitride materialsaretheoreticallyandexperimentallyinvestigatedtohighlightprosandcons ofeachtechnology.Thethirdsectionisdedicatedtothetransistormodelingathigh frequencies.Theattentionisfocusedontheextractionofequivalentcircuitmodels, whichrepresentagoodcompromisebetweenphysicalandbehavioralmodels.In fact,theequivalentcircuitmodelprovidesindispensablefeedbacktodevicetechnologistsforadvancingthetransistorfabricationprocessandisavaluabletooltocircuit designersforoptimizingcircuitperformance.Thebottom-upapproachfor equivalent-circuit-basedmodelingisdiscussed,startingwithadescriptionofhow toextractasmall-signalmodelinthefourthsection,beforemovingontoitsuse asacornerstonetodevelopbothnoiseandlarge-signalmodelsinthefifthandsixth sections,respectively.

1.2 MICROWAVETRANSISTORTECHNOLOGIES

Thefirstdemonstrationofafield-effecttransistor(FET)usingatwo-dimensional electrongas(2DEG)inapotentialquantumwellastheactivechannelwasmade in1980[1,2].ThistypeoftransistorwasnamedHEMTbytheJapaneseresearchers atFujitsuLaboratories.AlthoughHEMTisthemostpopularname,otherterms describingitsbasicoperationprinciplehavebeenproposedbyotherresearchgroups workingondevelopingthisnewtypeoftransistor.Examplesaremodulationdoped FET(MODFET,UniversityofIllinoisandRockwell,UnitedStates),twodimensionalelectrongasFET(TEGFET,ThomsonCSF,France),andselectively dopedheterojunctiontransistor(SDHT,BellLabs,UnitedStates).Sinceitsinception,theHEMThasreceivedworldwideattentionforitsattractiveadvantagescomparedtoitspredecessor,themetal-semiconductorfield-effecttransistor(MESFET): largergain,higheroperatingfrequency,andlowernoisefigure(NF).

ThebasicstructureofaHEMTconsistsofaheterojunctioncomposedofadoped wide-bandgapsemiconductorandanundopednarrow-bandgapsemiconductor.The earlierHEMTswerebasedonthealuminum-gallium-arsenide/gallium-arsenide (AlGaAs/GaAs)heterostructure.Commonly,n-channelGaAsFETsareconsidered, becauseelectronshavemuchhighermobilitythanholes.Asillustratedin Figure1.1, electronsdiffusefromthedopedwide-bandgapsemiconductortotheundoped narrow-bandone.Duetotheconductionbanddiscontinuityandtheaccumulation ofelectronsleavingpositivechargedionizeddopants,apotentialbarrierisformed attheinterfacebetweenthetwosemiconductors.Thisbarrierpreventstheelectrons fromgoingbacktothedopedsemiconductor.Therefore,a2DEGisconfinedina triangularpotentialquantumwell.Theseelectronsdriftinapurecrystallinematerial fromthesourcetothedrainandthespatialseparationofcarriersfromdonorsistypicallyimprovedbyintroducingathinspacerlayerofundopedAlGaAs.SuchaseparationallowsforachievingasignificantreductionofCoulombscatteringand carriersfrozenationizeddonors,whicharetwomechanismsresponsiblefordegradingthecarriertransportpropertiesatlowtemperature.Aconsiderableimprovement

Conduction band

Fermi level

TheenergybanddiagramforanAlGaAs/GaAsheterostructure.

oftheperformanceoftheHEMTisthusachievedatcryogenictemperatures,because thereductionofthephononscatteringprocessesatlowertemperaturesallowsfor obtainingaveryhighelectronmobility[3,4].Hence,electronsina2DEGexhibit amuchhighermobilitythanthoseinthedoped-channelMESFET,especiallyat lowtemperatures.

ThebasicoperationprincipleofaHEMTconsistsofcontrollingtheoutputdrain currentthroughthegatemodulationofthecarrierdensityinthe2DEG.Ifthegate biasisbelowthepinch-offvoltage,the2DEGchannelisdepleted.Asthegatevoltageisincreased,the2DEGdensityincreases,resultinginahigheroutputdraincurrent.Typically,aheavyforwardgatebiasisavoidedinordertopreventdevice degradationfromtheassociatedexcessiveconductioncurrentflowingthroughthe gateSchottkyjunction.Furthermore,ahigh VGS mayleadtotheoccurrenceof thephenomenonknownas“parasiticMESFET,”whichconsistsofatransconductancereductionduetoaparallelconductionthroughtheundepletedlowmobility AlGaAsdonorlayer[3].Infact,theincreaseof VGS lowersthepotentialenergybarrierandthen,byincreasing VDS,theelectronsofthe2DEGcangainenoughkinetic energyfromtheacceleratingelectricfieldinthechanneltosurmounttheAlGaAs/ GaAsenergybarrier.

ToimprovetheperformanceoftheconventionalAlGaAs/GaAsHEMT,an undopedlayerofnarrowbandgapindium-gallium-arsenide(InGaAs)canbeintroducedbetweentheAlGaAsandGaAslayers.InthecaseoftheAlGaAs/InGaAs/ GaAsstructure,thecarriersflowintheInGaAsquantumwellthatissquare-shaped. AstheInGaAsisnotlatticematchedtoitsadjacentlayers,theInGaAschannellayer hastobethinenoughsothatitstretchestofittheothertwosemiconductors.Compared totheconventionalHEMT,thistypeoftransistor,knownaspseudomorphicHEMT (pHEMT),exhibitsimprovedcarriertransportpropertiesduetothepresenceof indium,andabettercarrierconfinementduetoalargerbandgapdifference.

Doped AlGaAs

Undoped GaAs

Valence band

FIGURE1.1

Althoughsilicon(Si)ismuchcheaperthanGaAsbecauseofthelowerprocessing complexity,largerwaferdiameter,andbetterindustryinfrastructure,GaAshastraditionallybeenwidelyusedformicrowaveapplications.Afundamentalbenefitof usingGaAsconsistsofhigherelectronmobilityandsaturationvelocitycomparedwith thoseofSi.Furthermore,GaAsbeingintrinsicallyaverypoorconductorofferssemiinsulatingsubstrates,whileSisubstratesaremuchmoreconductive.Althoughsiliconon-insulator(SOI)technologywithahighresistivitysubstrateallowsforminimizing thesubstratelosses,theSOIwafershavethedrawbacksofhavinghigherwafer cost,lowerthermalconductivity,andhigherdefectdensitythanbulkSiwafers.Hence, GaAsisveryusefulformicrowaveandmillimeter-waveintegratedcircuits(MMICs), whereactiveandpassivecomponentshavetobefabricatedonthesamesemiconductor substrate.ThisisbecausetheGaAssemi-insulatingsubstrateallowsforachieving electricalisolationamongthevariouscomponents,whileeffectiveshieldingsolutions areneededforSi-basedradio-frequencyintegratedcircuits(RFICs).

MMICshavesignificantadvantagesoverhybridcircuitssuchassmallersize, lighterweight,improvedreproducibilityandreliability,broaderbandperformance, andlowercostformassproduction.AlthoughtheinterestinmilitaryandspacecommunicationsystemshasdrivenandcontinuestodrivethedevelopmentofMMIC technology,MMICsarenowalsousedincivilapplications,suchasmobile telephony.

Tomeetthedemandingrequirementsforwirelesscommunicationsystemssuch asthoseforbasestations,alotofattentioniscurrentlydevotedtotheHEMTbased onthealuminum-gallium-nitride/gallium-nitride(AlGaN/GaN)heterostructure.The GaN-basedHEMTisundoubtedlytheleadingtechnologyformicrowavehigh-power applications[5–19]becausethewidebandgapofthenitridesemiconductorsimplies ahigherbreakdownvoltage.InthecaseofGaN-basedHEMTs,thephysicsbehind theformationof2DEGissubstantiallydifferentfromtheoneillustratedin Figure1.1 forconventionalGaAs-basedHEMTs.Owingtothelargepiezoelectricandspontaneouspolarizationeffectsandthelargeconductionbanddiscontinuitybetweenthe AlGaNbarrierandtheGaNchannellayers,anextremelyhigh2DEGdensitycanbe achievedevenwithoutintentionallydopingtheAlGaNlayer.Theelectricfieldassociatedwiththepiezoelectricandspontaneouspolarizationscanbehighenoughtoionizeelectronsandforcethemtodrifttowardstheheterointerfacewheretheyfallintothe quantumwell,formingthe2DEG.Inthecaseofunintentionallyintroduceddopant impurities,the2DEGconsistsofelectronsresultingfromcovalentelectrons,impuritiesthathappentobepresentinthematerials,andlooselybondedsurfaceelectrons.

GaNHEMTsaretypicallygrownonsiliconcarbide(SiC),silicon,orsapphiresubstrates.Siliconisavailableinlargerwafersizesandischeaperthantheothertwosubstrates.Ontheotherhand,siliconcarbideisthemostexpensivesolution,butits superiorthermalconductivitywithrespecttosiliconandsapphiremakesitverysuitableforhigh-powerandhigh-temperatureapplications.Infact,high-powerdevices needasubstratematerialwithhighthermalconductivitytospreadheatefficiently.

TopresentexperimentalresultsasanillustrativeexampleoftheSiCtechnology, Figure1.2 showsthebehaviorof ID versus VDS and VGS foranAlGaN/GaNHEMT

FIGURE1.2

Behaviorof ID(VDS, VGS)fora0.7 800 μm2 GaNHEMTat20°C.

Drain-source voltage (V) 051015202530

FIGURE1.3

Outputcharacteristics ID(VDS)fora0.7 800 μm2 GaNHEMTat VGS ¼ 2Vunderthree differentambienttemperatures:20°C (solidblackline),50°C (dashedblackline),and80°C (solidgrayline)

onSiCsubstratewithagatelengthof0.7 μm[20].Toavoiddevicedegradation,the maximum VDS andthemaximumdissipatedpower Pmax havebeenlimitedto28V and5W/mm,respectively.Ascanbeobserved,thedeviceexhibitsanegativeslope of ID(VDS)underhighlydissipatedpowerconditionsbecauseoftheself-heating phenomenon.

Figure1.3 reports ID(VDS)at VGS ¼ 2Vunderthreedifferentambienttemperatures:20°C,50°C,and80°C.Itisobservedthattheself-heatingeffectisenhancedat highertemperaturesanddissipatedpower,duetotheassociatedincreaseofthephononscatteringprocessesleadingtoadegradationoftheelectrontransportproperties. Furthermore, Figure1.4 showstheloadlinesat1dBgaincompressionata fundamentalfrequency f0 of2GHzunderthethreeambienttemperatures.

FIGURE1.4

Loadlinesat1dBcompressionwithafundamentalfrequencyof2GHzfora0.7 800 μm2 GaNHEMTat VGS ¼ 2Vand VDS ¼ 19.5Vunderthreedifferentambienttemperatures: 20°C (solidblackline),50°C (dashedblackline),and80°C (solidgrayline)

FIGURE1.5

Cryogenicsystemformicrowavetransistorcharacterization.

Asexpected,theswingoftheloadlinedecreasesathighertemperaturesandthis impliesareductionoftheoutputpower.

Figure1.5 showsapictureofanexperimentalset-upformicrowavetransistorcharacterizationatcryogenictemperatures.Thecryogenicsystemisbasedonaclosedcircleliquidheliumrefrigeratorandavacuumchamberhavingmicrowavecoaxial feedthroughsforconnectingtheexternalinstrumentation.Thetemperatureismonitoredandcontrolledbyusingaproportional-integral-differentialcontrolloop.ToillustratetheperformanceofacryogenicallycooledHEMT, Figure1.6 showsthebehavior ofthemagnitudeoftheforwardtransmissionparameterS21 forapackagedAlGaAs/ InGaAs/GaAspHEMT(MitsubishiMGF4919)versusfrequencyand VGS attwo differenttemperatureconditions:16.85°Cand 243.15°C[3].Bycoolingthe

FIGURE1.6

Magnitudeof S21 versusfrequencyand VGS foraGaAspHEMT(MitsubishiMGF4919) at VDS ¼ 2Vundertwodifferentambienttemperatures:16.85°C (whiteplot) and 243.15°C (grayplot).

transistor,themagnitudeof S21 increaseswhen VGS isfarfrompinch-off,whileit decreaseswhen VGS isnearpinch-off.Theobservedbehaviorofthisfigureofmerit isduetothefactthat,bydecreasing VGS towardsthepinch-off,thethresholdvoltage (VTH)shifthasastrongerimpacton S21 thantheimprovementoftheaverageelectron velocity.Itshouldbeemphasizedthattheinfluenceofthethresholdvoltageshifton S21 mightbecompensatedbytheDCbiascircuitrywhenthedeviceisbiasedbyimposing ID ratherthan VGS [21].Itshouldbenotedthatexceptforthisdeviceinapackage,allof thetransistorsanalyzedinthischapterareon-waferdevices.

1.3 TRANSISTORMODELING

Whatismicrowavetransistormodeling?Itconsistsofthefieldofknowledgeand problem-solvingconcernedwithhowtoextract,implement,andvalidatemodels abletodescribethepropertiesofadvancedtransistorsmeantforhigh-frequency applications.Itisworthpointingoutthattheextractedmodelshavetobeproperly implementableinacircuitsimulatorandbeaccuratelyvalidatedbymeansofsuitable measurementspriortotheirrelease.Theimportanceofthisresearchbranchcomes fromtheneedformodelsashelpfulfeedbacktotechnologistsforadvancingtransistorfabricationandasaneffectivetoolforcircuitdesignersoptimizingcircuitperformance.Althoughmanysuccessfulmodelingtechniqueshavebeendevelopedinthe lastdecades,microwavetransistormodelingisanevergreenresearchfieldthatstill attractsextensiveinterest.Thisisbecauseinnovativetechniquesareconstantly requiredtomodelthelatestandcontinuouslyprogressingtransistortechnologies.

Asillustratedin Figure1.7,transistormodelscanbedividedintothreemaincategories:physicalmodels[22–25],behavioralmodels[26–29],andequivalentcircuit models[30–33].Thephysicalmodels(or“transparentboxes”)arebasedonthestudy ofthephysicalphenomenaoccurringwithinthetransistor,whilethebehavioral

Classificationofthetransistormodelsintophysicalmodels(or transparentboxes),equivalent circuits(or grayboxes),andbehavioralmodels(or blackboxes).

models(or“blackboxes”)arebasedontheexperimentalcharacterizationofthe behavioralinput-outputdescriptionsofthetransistor.Aneffectivecompromise betweenphysicalandbehavioralmodelsisrepresentedbytheequivalentcircuits (or“grayboxes”),whichareextractedfromexperimentalmeasurements,yetkeeping theconnectionwiththeinnerphysicsofthetransistor.Equivalentcircuitmodelsgive thetechnologistsbetterfeedbackthanblack-boxmodelsandenablecircuitdesigners todomuchfastersimulationsthanwithphysicalmodels.Infact,physicalmodelsare notreallysuitableforcomputer-aideddesign(CAD)environmentsduetotheirprohibitivesimulationtime.Ontheotherhand,behavioralmodelsattransistorlevel requireexpensivemeasurementsandtheyshowgoodpredictivecapabilitiesonly intheregimeoftheircharacterization.Itisworthnotingthatbehavioralmodels atcircuitandsystemlevels,wherequiescentconditionandimpedanceenvironment (typically50 Ω)areaprioriknown,donotshowthesamelimitationspreviouslydiscussed,andhavebeensuccessfullyandincreasinglyusedbydesignersinthe lastyears.

Thepresentchapterfocusesonmicrowavetransistormodelingbasedonthe equivalentcircuitrepresentation.Equivalent-circuit-basedtransistormodelingis aninterdisciplinaryscientificresearchfieldthatrequiresexpertisefromdifferent areas:semiconductordevicephysics,electromagneticfields,microwavemeasurementtechniques,circuitnetworktheory,andcircuitsimulationsoftwarepackages. Althoughthemicrowaveperformanceofatransistorcanbefullyandstraightforwardlycharacterizedbycarryingouthigh-frequencymeasurementswithdedicated instrumentations,itisveryusefultoextractanequivalentcircuitmodel,asitisa physicallymeaningfulandaverycompactrepresentation,alsoallowingafastestimationofthescalingofthedeviceperformance.

Theselectionoftheappropriatetopologyoftheequivalentcircuitformodeling thespecifictestedtransistorisachallengingtask,sinceahighernumberofcircuit elementsmayallowforobtainingmoreaccurateresults,butthecircuitcomplexity becomeshigheraswellastheriskofphysicalinconsistency.Hence,thenumberof circuitelementsshouldbetherighttrade-offbetweenmodelaccuracy,physical

FIGURE1.7

soundness,andcomplexity.Typically,thefirstmodelingstepconsistsofextractinga small-signalequivalentcircuitthat,subsequently,canbeusedasacornerstonefor buildingbothnoiseandlarge-signalmodels.Theremainderofthischapterisdedicatedtosmall-signal,noise,andlarge-signalmodeling.GaAsandGaNHEMTsare usedasreferencedevicestoillustratetheapplicationofequivalentcircuitmodeling techniqueswithexperimentalresults.

1.4 SMALL-SIGNALMODELING

Figure1.8 showsanexampleofasmall-signalequivalentcircuittopologyfora HEMT.Theresistances Rgsf and Rgdf areoftenomittedastheconductiongatecurrent isnegligibleundertypicaloperatingbiasconditions.Typically,thevaluesoftheelementsaredeterminedusingscattering(S-)parametermeasurements,whichcanbe straightforwardlyandaccuratelymeasuredbymeansofavectornetworkanalyzer (VNA).Givenabiascondition,themodelextractionisbasedondefiningeightequationsthatrepresentthefourcomplex S-parametersintermsoftheequivalentcircuit elementsateachfrequency.Severaltechniqueshavebeendevelopedtosolvethisillconditionedproblemandtheycanbeclassifiedintotwomaincategories:numerical optimization[34–36]andanalyticaltechnique[33,37,38].However,itiswellknown thatoptimizationmethodscanleadtocircuitelementvalueswithnophysicalmeaningandbywhichtheresultscandependonmanyfactors(eg,thestartingelement values,localminima,andtheoptimizationmethoditself).Ontheotherhand,analyticalmethodsallowovercomingthesedrawbacksbysplittingthemodelextraction intwoparts.Basically,theequivalentcircuitelementsareusuallydividedinto twomaingroups:theextrinsicelements(ie, Cpg, Cpd, Lg, Ls, Ld, Rg, Rs, Rd)andintrinsicones(ie, Cgs, Cgd, Cds, Rgsf, Rgdf, Rgs, Rgd, Rds, gm, τ ).Theformerareassumed

circuit

FIGURE1.8

tobebias-independent,whereasthelatteraredependentonthebiascondition.The analyticaltechniquesarebasedondeterminingfirsttheextrinsicelementsandsuccessivelytheintrinsicones.

Generally,theextrinsicelementsareobtainedfrom“cold” S-parametermeasurements(ie, VDS ¼ 0V)[33,37–48],becausethe“cold”conditionallowsasignificant simplificationoftheequivalentcircuitmodel.Theterm“cold”arisesfromthefact thattheequivalenttemperature,representingthecarrieraveragekineticenergy,is coldcomparedtothetypicaloperatingconditionandthedissipatedpowerisnull. With VDS equaltozero,thevoltagecontrolledcurrentsourcecanbeomittedsince therearenocarriersdriftingfromsourcetodrain.Asaresult,twounknowns(ie, gm and τ )disappearbut,atthesametime,twoequationsvanish(ie, S12 ¼ S21),duetothe factthatundercoldconditionthetransistorbehavesasareciprocalnetworkwith [S] ¼ [S]T (ie,notcontaininganynonreciprocalmediasuchasferritesorplasmas, oractivedevices).Additionally,thezerodrain-sourcevoltageallowsassumingthat thegate-sourceandgate-drainintrinsiccircuitsareequal. Figure1.9 showsthatthe intrinsiccoldHEMTcanberepresentedbyan RC parallelnetwork(Ry, Cy)modeling theSchottkygatejunctionandtwoidentical RC parallelnetworks(Rch/2,2Cch) modelingtheactivechannel.Astheintrinsicresistancesdecreaseathigher VGS, theintrinsiccapacitancesarenegligibleunderforwardcondition,whereastheintrinsicresistancesarenegligibleunderpinch-offcondition[40].Ingeneral,theextrinsic capacitancesareextractedfromIm(Yij)ofthecapacitivenetworkrepresentingthe

FIGURE1.9 Small-signalequivalentcircuitfora“cold”HEMT.

transistoratlowfrequenciesunderpinch-offcondition,whereastheextrinsicinductancesandresistancesare,respectively,obtainedfromRe(Zij)andIm(Zij)of theresistiveinductivenetworkrepresentingthetransistorathighfrequenciesunder high VGS.

Afterde-embeddingtheextractedextrinsiccontributionsfromthe S-parameter measurementswithsimplematrixmanipulations[49],theintrinsicelementscan becalculatedfromtheintrinsic Y-parameters.Inparticular, Rgsf and Rgdf areestimatedfromtherealpartoftheintrinsic Y11 and Y12 atlowfrequenciesbyassuming thatthecapacitancesbehaveasopencircuits[50]:

Therefore,theextractedvaluesof Rgsf and Rgdf canbesubtractedand,finally,the remainingeightintrinsicelementscanbecalculatedfromtherealandimaginary partsofthefour Y-parameterswithstandardformulas[51].Itshouldbehighlighted that Rgsf and Rgdf playasignificantroleonlyatrelativelyhigh VGS whenforward biasingthegateSchottkyjunction.Thisisconfirmedby Figure1.10 showingthebias

Behaviorof Ggsf (A)and Ggdf (B)versus VDS and VGS fora0.2 100 μm2 GaNHEMT.

FIGURE1.10

dependenceofthetwoconductancesassociatedto Rgsf and Rgdf foraGaNHEMTon sapphiresubstratewithagatelengthof0.2 μm.

Itisworthnotingthattheanalysisoftheintrinsic Y-parametersversusfrequency cansuggesttoaddand/ortoneglectsomeintrinsiccircuitelements.Infact,differencesamongtechnologies,materials,structures,andstudiedfrequencyrangesare reflectedindifferentequivalentcircuittopologies.Forinstance,thepresentanalysis isfocusedontheintrinsic Y22 tohighlighttheimportanceofdeterminingthemost appropriatecircuittopology.Thepresenceofthefeedbackresistance Rgd allows definingthisadmittanceparameterasfollows:

Then,therealandimaginarypartsoftheintrinsic Y22 canbeexpressedasfollows:

Eq. (1.4) showsthat Rgd hastobeincludedinthemodelwhenRe(Y22)tendsto increasewithfrequencyinsteadofremainingconstantandequalto gds.Contrary tothebehaviorpredictedbyEq. (1.4), Figure1.11 showsthattheintrinsic Re(Y22)decreasesathigherfrequenciesforaGaAspHEMTwithagatelengthof 0.25 μm.Consequently,tomodelthisobservedbehavior, Rgd hasbeenomitted and gds hasbeenreplacedbyavoltagecontrolledcurrentsourcewithatimedelay τ ds.Thatsolutionallowsdefining Y22 asfollows[41]:

Hence,therealandimaginarypartsoftheintrinsic Y22 aregivenby:

Eq. (1.7) showsthat τ ds isrequiredtomodelthedecreaseofRe(Y22)athigherfrequencies(see Figure1.11).When ωτ ds issufficientlysmall, τ ds canbeapproximated withaninductance Lds inserieswith gds.However,incontrastwiththe Lds implementation, τ ds allowsthesimulationalsoofnegativevaluesofRe(Y22)[41].

Toverifytheaccuracyoftheextractedequivalentcircuit,themodelshouldbeable toreproducethe S-parametermeasurements.Furthermore,therobustnessofthemodel shouldbeconfirmedbyitsvalidationunderawiderangeofoperatingconditions. Inparticular,thecircuitelementsareexpectedtobephysicallymeaningfulandthus theirvaluesshouldbeanalyzedversusbiascondition,temperature,andgeometrical dimensionstocheckifthemodelmeetsthephysicalexpectations.Asanillustrative example, Figure1.12 reportsthegoodagreementbetweenmeasuredandsimulated

Y 22 ) (mS) Frequency (GHz) 4 2 0 –2 0102030405060708090 0

FIGURE1.11

Comparisonbetweenmeasured (symbols) andsimulated (lines) intrinsic Y22 from4to 90GHzfora0.25 300 μm2 GaAspHEMTat VGS ¼ 0.65Vand VDS ¼ 10V.Simulationsare obtainedwith(A)andwithout(B)accountingfor τ ds

S-parametersforaGaAspHEMTwithagatelengthof0.15 μm[52].Thevalidationis performedunderdifferentbiasconditionsincludingnegative VDS,becausethetested deviceismeantforcold-FETmixerdesign.Itshouldbehighlightedthatthestandard formulasforidentifyingthecurrentsourceatpositive VDS havetobemodifiedforthe extractionatnegative VDS:thesignof gm hastobechangedandthis π phaseshifthasto besubtractedbeforecalculating τ .Theachievedbiasdependenceof gm and Cgs is reportedin Figure1.13.

Figure1.14 shows gm and Cgs versus VGS foraGaAspHEMTat VDS ¼ 2Vunder twodifferenttemperatureconditions:16.85°Cand 243.15°C[4].Inagreement withtheobservedbehaviorofthemagnitudeof S21 (see Figure1.6),thetesteddevice showsthattheimprovementofthecarriertransportpropertiesatcryogenictemperatureleadstoanincreaseof gm onlywhen VGS isfarfrompinch-off.With VGS 4 2 0 0102030405060708090 –2 0

FIGURE1.12

Comparisonbetweenmeasured (symbols) andsimulated (lines)S-parametersfrom2.5to 65GHzfora0.15 300 μm2 GaAspHEMTat: VDS ¼ 0Vand VGS ¼ 1V(A), VDS ¼ 0.5Vand VGS ¼ 0.8V(B), VDS ¼ 0.5Vand VGS ¼ 0.5V(C).

FIGURE1.13

Behaviorof gm (A)and Cgs (B)versus VDS and VGS fora0.15 300 μm2 GaAspHEMT.

FIGURE1.14

Behaviorof gm (A)and Cgs (B)versus VGS foraGaAspHEMT(MitsubishiMGF4919) at VDS ¼ 2Vundertwodifferentambienttemperatures:16.85°C (blacksymbols) and 243.15°C (whitesymbols)

decreasingtowardsthepinch-offregion,the VTH shiftleadstoadegradationof gm at lowertemperatures.Sucha VTH shiftcanbeattributedtothereductionofthenet positivechargeunderthegate,duetoadecreaseofthethermallyactivatedelectron detrappingmechanismsoccurringwithintheAlGaAsdonorlayer.Asaresultofthis reductionofthedetrappingphenomena,adecreaseofthe“equivalent”dopinglevel canberesponsiblefortheobservedreductionof Cgs atlowertemperatures[4].

Theconventionalscalingrulesarebasedontheassumptionthatincreasingthe gatewidthcanbeseenasconnectingmoreintrinsictransistorsinparallel.Hence, theintrinsicequivalentcircuitelementsassociatedwithadmittances(ie,capacitancesandconductances)andthedraincurrentitselfshouldbeproportionalto thetotalgatewidth,whiletheintrinsiconesassociatedwithimpedances(ie,inductancesandresistances)shouldbeinverselyproportionaltothisgeometricdimension,andtheintrinsictimedelayshouldbeconstant.Nevertheless,thisisan oversimplifiedassumptionthatfailstotakeintoaccountcomplexphenomenasuch asthermaleffects,bordereffects,andresidualextrinsicelementcontributions.As illustrativeexample, Figure1.15 shows g

FIGURE1.15

Behaviorof gm, gds (A), Cgs, Cgd, Cds (B),and τ (C)versusthegatewidthforthreeGaAs HEMTs(0.25 100 μm2,0.25 200 μm2,and0.25 300 μm2)at VGS ¼ 0.6Vand VDS ¼ 2.5V.

widthforthreeAlGaAs/GaAsHEMTswithagatelengthof0.25 μm.As expected,aquiteclearlinearbehaviorw ithrespecttothegatewidthisobserved in gm, g ds , Cgs , C gd ,and C ds ,while τ isalmostindependentofthegatewidth. Thisisbecause τ canbecorrelatedtothecarrie rtransittimeand,therefore, dependsmainlyonthegatelength(infirs tapproximation,proportionally).As canbeseenin Figure1.16A ,thelineapproximating gm versusthegatewidth exhibitsapositiveinterceptwhen V GS isincreasedto0V.Thisresultcanbe attributedtothefactthatthethermalphenomenaareenhancedintransistorswith largergatewidthandathigher V GS ,duetothehigherdissipatedpower.Tocorroboratethisobservation, g m isnormalizedwithrespecttothegatewidthin Figure1.16B andtheachievedvalueisevidentlyreducedinlargertransistors. Byconsideringthatthethermalphenomenacannotfollowtheappliedsmallsignalatsuchhighfrequencies,theobserveddegradationofthenormalizedRF g m hastobeascribedtotheeffectsofthermalphenomenaduetotheDC dissipatedpower.

FIGURE1.16

Behaviorof gm (A)anditsnormalizedvalue(B)versusthegatewidthforthreeGaAsHEMTs (0.25 100 μm2,0.25 200 μm2,and0.25 300 μm2)at VGS ¼ 0Vand VDS ¼ 2.5V.