Table Of Content

FEBRUARY2009 VOLUME57 NUMBER2 IETMAB (ISSN0018-9480) PAPERS LinearandNonlinearDeviceModeling ScalableEquivalentCircuitFETModelforMMICDesignIdentifiedThroughFW-EMAnalyses.......................... ................................................................. D.Resca,A.Raffo,A.Santarelli,G.Vannini,andF.Filicori 245 AnalyticalExtractionofExtrinsicandIntrinsicFETParameters ....................B.L. Ooi,Z.Zhong,andM.-S.Leong 254 AComprehensiveAnalysisofAM–AMandAM–PMConversioninanLDMOSRFPowerAmplifier.................... ...................................................................................................... J.P.AikioandT.Rahkonen 262 ABroadbandandScalableLossySubstrateModelforRFNoiseSimulationandAnalysisinNanoscaleMOSFETsWith VariousPadStructures .............................................................................. J.-C.GuoandY.-H.Tsai 271 ANonlinearElectro-ThermalScalableModelforHigh-PowerRFLDMOSTransistors..................................... ................................ J.Wood,P.H.Aaen,D.Bridges,D.Lamey,M.Guyonnet,D.S.Chan,andN.Monsauret 282 SmartAntennas,PhasedArrays,andRadars ACircularlyPolarizedBalancedRadarFront-EndWithaSingleAntennafor24-GHzRadarApplications ............... ................................................................................... C.-Y.Kim,J.-G.Kim,D.Baek,andS.Hong 293 ActiveCircuits,SemiconductorDevices,andICs DesignandAnalysisfora60-GHzLow-NoiseAmplifierWithRFESDProtection .......................................... ................................... B.-J.Huang,C.-H.Wang,C.-C.Chen,M.-F.Lei,P.-C.Huang,K.-Y.Lin,andH.Wang 298 A50–300-MHzHighlyLinearandLow-NoiseCMOS - FilterAdoptingMultipleGatedTransistorsforDigitalTV TunerICs......................................................................................K.Kwon,H.-T.Kim,andK.Lee 306 Optimizing Losses in Distributed Multiharmonic Matching Networks Applied to the Design of an RF GaN Power AmplifierWithHigherThan80%Power-AddedEfficiency.......................... M. HelaouiandF.M.Ghannouchi 314 DigitalBasebandPredistortionBasedLinearizedBroadbandInverseClass-EPowerAmplifier ............................ ............................................................................................. M.Thian,M.Xiao,andP.Gardner 323 0.5-V5.6-GHzCMOSReceiverSubsystem .................... H.-C.Chen,T.Wang,H.-W.Chiu,T.-H.Kao,andS.-S.Lu 329 The Effects of Limited Drain Current and On Resistance on the Performance of an LDMOS Inverse Class-E Power Amplifier .................................................................................. F.You,S.He,X.Tang,andX.Deng 336 (ContentsContinuedonBackCover) (ContentsContinuedfromFrontCover) SignalGeneration,FrequencyConversion,andControl LowPhaseNoiseSelf-SwitchedBiasingCMOSLCQuadratureVCO ............................ G.HuangandB.-S.Kim 344 FieldAnalysisandGuidedWaves HighlyEfficientGroupingStrategyfortheAnalysisofTwo-PortArbitrarilyShaped -PlaneWaveguideDevices ...... ..........................Á.BelenguerMartínez,H.EstebanGonzález,V.E.BoriaEsbert,C.Bachiller,andJ.V.Morro 352 CADAlgorithmsandNumericalTechniques BroadbandModelingofHigh-FrequencyMicrowaveDevices........D.Paul,M.S.Nakhla,R.Achar,andA.Weisshaar 361 SurfaceInteractionMatricesforBoundaryIntegralAnalysisofLossyTransmissionLines ................................. .................................................................................................. A.SiripuramandV.Jandhyala 374 AcceleratedMicrowaveDesignOptimizationWithTuningSpaceMapping .................................................. .............................................................. S.Koziel,J.Meng,J.W.Bandler,M.H.Bakr,andQ.S.Cheng 383 An Efficient Perturbative Approach for Finite-Element Analysis of Microwave Devices Exhibiting Small Geometrical Variations .................................................................. G. Guarnieri,G.Pelosi,L.Rossi,andS.Selleri 395 WaveguideMicrowaveImaging:NeuralNetworkReconstructionofFunctional2-DPermittivityProfiles................. ................................................................................ A.V.Brovko,E.K.Murphy,andV.V.Yakovlev 406 EfficientAlgorithmforPassivityEnforcementof -Parameter-BasedMacromodels......................................... ..................................................................................... T.Dhaene,D.Deschrijver,andN.Stevens 415 AMultiple-LineDoubleMultirateShootingTechniquefortheSimulationofHeterogeneousRFCircuits................. .................................................................................................... J.F.OliveiraandJ.C.Pedro 421 FiltersandMultiplexers ApplicationofRepresentationTheorytoDual-ModeMicrowaveBandpassFilters ................................ S.Amari 430 Packaging,Interconnects,MCMs,Hybrids,andPassiveCircuitElements Wire-BondFreeTechniqueforRight-AngleCoplanarWaveguideBendStructures .... H.KimandR.Franklin-Drayton 442 AnalyticalSolutionforVoltage-StepResponseofLossyDistributedRCLines ................ A. PunningandE.Jalviste 449 InstrumentationandMeasurementTechniques NoninvasiveProcedureforMeasuringtheComplexPermittivityofResins,Catalysts,andOtherLiquidsUsingaPartially FilledRectangularWaveguideStructure ........................................M.J. Akhtar,L.E.Feher,andM.Thumm 458 ABroadbandandStableMethodforUniqueComplexPermittivityDeterminationofLow-LossMaterials................ ................................................................................................. U.C.HasarandC.R.Westgate 471 Microwave Photonics SpaceMappingWithAdaptiveResponseCorrectionforMicrowaveDesignOptimization .................................. ........................................................................................ S.Koziel,J.W.Bandler,andK.Madsen 478 AnInvestigationoftheOperationandPerformanceofCoherentMicrowavePhotonicFilters............................... ...................................................................................................... B.C.PileandG.W.Taylor 487 ChirpedMicrowavePulseCompressionUsingaPhotonicMicrowaveFilterWithaNonlinearPhaseResponse .......... ............................................................................................................... C.WangandJ.Yao 496 MicrowaveFrequencyMeasurementBasedonOpticalPowerMonitoringUsingaComplementaryOpticalFilterPair .. ....................................................................................................... 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DigitalObjectIdentifier10.1109/TMTT.2009.2014682 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 245 Scalable Equivalent Circuit FET Model for MMIC Design Identified Through FW-EM Analyses Davide Resca, Member, IEEE, Antonio Raffo, Member, IEEE, Alberto Santarelli, Member, IEEE, GiorgioVannini, Member, IEEE, and FabioFilicori Abstract—A scalable approach to the modeling of millimeter- gatefingers)forthespecificapplicationthroughtheevaluation wavefield-effecttransistorsispresentedinthispaper.Thisisbased ofsuitablydefinedfiguresofmeritanddesigncriteria[1],[2]. on the definition of a lumped extrinsic parasitic network, easily Scalablemodelsalsoallowforimportanttimesavingduringthe scalablewithboththenumberoffingersandthefingerwidths.The empiricalcharacterizationoffoundryprocesses. identificationoftheextrinsicnetworkparametersiscarriedoutby meansofaccuratefull-waveelectromagneticsimulationsbasedon Linear scaling rules are widely adopted for the intrinsic de- thelayoutofasinglereferencedevice. vice, providing accurate prediction results [3] up to relatively Inthepaper,theparasiticeffectsofthegate/drainmanifoldsand high frequencies. However, when microwave and millimeter- of the source layout are investigated, leading to the definition of wave applications are involved, the overall quality of an elec- realisticlinearscalingrules. tron device model also strongly depends on the rules applied The obtained model is experimentally validated by using a familyof0.25- mmillimeter-waveGaAspseudomorphicHEMTs tothescalingoftheextrinsicnetwork,describingtheparasitic throughtheaccuratepredictionofcriticalperformanceindicators, phenomena taking part in the physical interconnections of the suchasthelinearmaximumpowergainorthestabilityfactor. intrinsicdevicetotheexternallyaccessibleterminals. Despitethesimplicityoftheproposedmodel,itprovestobeas Simple linear scaling rules [4], [5] applied to conventional accurateastypicalscalablemodelsprovidedbyfoundries. lumped parasitic networks do not lead to accurate scalable Straightforwardapplicationofthescalablemodelingapproach to the optimum device geometry selection in a typical design models at high frequencies. Complex, technology-dependent problemisalsopresented. scalingrules[6]–[9]orquasi-distributedmodels[10]–[19]have beenrecentlyproposedintheliteratureinordertoimprovethe IndexTerms—Electromagnetic(EM)analysis,field-effecttran- high-frequencypredictionaccuracyofscaleddevicemodels. sistors(FETs),microwaveandmillimeter-waveintegratedcircuits (MMICs),semiconductordevicemodeling. Commercialfull-waveelectromagnetic(FW-EM)simulators have been also recently exploited (e.g., see [18] and [19]) for theanalysisofextrinsicparasiticphenomenaandthedefinition I. INTRODUCTION ofdistributedmodelingapproaches,wheretheentireactivearea isdividedintoasuitablenumberofelementary“activeslices.” Suchmodelingapproacheshavebeenprovenverysuitable for M ICROWAVE AND millimeter-wave integrated circuit scaling, providing extremely accurate electrical response pre- (MMIC) design requires empirical models, which ac- dictions. Unfortunately, their exploitation in conjunction with curately describethelinearand nonlinearbehavior ofelectron nonlinearmodelsoftheactiveslicesleadstorelativelypoornu- devicesuptoextremelyhighfrequencies.Whenembeddedinto mericalefficiencyinharmonicbalance(HB)analysesduetothe circuit schematics, accurate device models allow engineers to proliferationinthenumberofinternalnonlinearports. design and optimize the circuit performance before the actual In this paper, an almost conventional lumped parasitic net- fabrication. work is adopted. However, a new simple parameter identifica- Optimum device periphery selection in actual design tasks tionprocedureisproposedonthebasisofanFW-EMsimulation oftenrequiresadifferentmodelforeachparticulardevicelayout ofthedevicelayout.Inaddition,suitablerulesareprovidedfor inagiventechnologicalprocess.Inordertoavoidthisproblem, improvedpredictionaccuracyofscaleddevices.Typicaldevice empiricalscalablemodelsareavailableallowingthedesignerto geometricalparameters, suchasthenumberoffingersandthe selecttheoptimumdevicegeometry(i.e.,numberandwidthof unitgatewidth,maybeusedbythedesignerassweptandeven optimizationvariablesbymeansoftheproposedapproach.Al- ManuscriptreceivedApril26,2008;revisedSeptember23,2008.Firstpub- though this paper deals with linear models, the proposed ap- lishedJanuary19,2009;currentversionpublishedFebruary06,2009.Thiswork proach is totally suitable for the application of scalable non- wassupportedinpartbytheItalianMinistryofUniversityandResearch(MUR). linearmodelstotheintrinsicdevice. D. Resca, A. Santarelli, and F. Filicori are with the Department of Elec- tronics, Computer Sciences and Systems, University of Bologna, 40136 This paper is organized as follows. The proposed lumped Bologna, Italy (e-mail: [email protected]; [email protected]; parasitic network is introduced in Section II-A and the cor- ffi[email protected]). responding scaling rules are also discussed. With respect to A.RaffoandG.VanniniarewiththeDepartmentofElectronics,University of Ferrara, 44100 Ferrara, Italy (e-mail: [email protected]; giorgio.van- the somehow similar approach presented in [20], the effects [email protected]). of widening (or shrinking) of the gate and drain manifolds in Colorversionsofoneormoreofthefiguresinthispaperareavailableonline thepresenceofahigher(orlower)numberoffingersaretaken athttp://ieeexplore.ieee.org. DigitalObjectIdentifier10.1109/TMTT.2008.2011208 into account here and a new scaling rules are provided for the 0018-9480/$25.00©2009IEEE 246 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 Fig.2. Lumpedcomponentnetworkdescribingthedeviceextrinsicparasitic phenomena.Schematicregions(I)–(IV)arestrictlyrelatedtothecorresponding Fig.1. Deviceparasiticeffectssubdivisionthroughdevicelayoutconsidera- layoutregionsshowninFig.1. tions.Gateanddrainmanifolds(I),sourcevia-holes(II),airbridge(III),and fingerregion(IV)areshown. effort could be required if parasitic phenomena are expected to strongly affect these regions. It is worth noting that, the manifold and source parasitic components. The new scaling parasitic phenomena located in the doped layers have been rulesleadtocriticalimprovementinthepredictionaccuracyof considered fully negligible in the case of the 0.25- m GaAs scaled devices. pHEMTusedinthisstudy.Experimentalvalidationprovidedin Anewprocedurefortheidentificationofthelumpedcompo- SectionIIIempiricallyconfirmsthevalidityofthisassumption. nentsoftheparasiticnetworkisthenpresentedinSectionII-B. Inordertogetproperscalingrulesofthemodel,thedevice This is based on a three-step process aimed at the separation layoutinFig.1isseparatedintofourdifferentregions.Region oftheentireequivalentcircuitparameter(ECP)setintosmaller (I) accounts for the parasitic effects due to the gate and drain groups, more easily identifiable through the fitting of simpler manifolds, which feed the signals to each finger. Region (II) FW-EMsimulations. accounts for the parasitic effects due to the via-holes, which Experimental validation of the model is proposed in provides source connections to ground. Region (III) accounts Section III. A family of 0.25- m GaAs pseudomorphic for the airbridge, which providethe ground connection tothe HEMTs (pHEMTs) is fully characterized and scaled models sourcefingersthroughthevia-holepads.Region(IV)accounts are obtained from a reference device. In order to meet the de- fortheparasiticeffectsduetotheinteractionsbetweenthefinger signerpointofview,theevaluationofthepredictionaccuracyof metallizations(i.e.,ohmiclossesalongthegateanddrainfingers thescaledmodelsiscarriedoutdirectlyonthebasisofcritical and capacitive-like couplings both between the gate and drain performance indicators, such as the maximum available gain fingers themselves and between the gate/drain fingers and the (MAG),andthestabilityfactor [21].Despitethesimplicityof airbridge). the proposed approach, improvements in accuracy are proven This somehow intuitive separation leads to the lumped ex- in comparisonswith other similarapproaches [20] and typical trinsicparasiticnetworkshowninFig.2. foundrymodels. Thefourelements , , ,and (whereMde- Finally, a practical example of optimum device periphery notesmanifold)modeltheparasiticeffectsofthelayoutregion selection by means of the proposed approach is provided in (I).Theelements and modeltheeffectsofthevia-holes Section IV. Advantages with respect to other conventional andtheairbridgeinlayoutregions(II)and(III).Asdiscussed scalable device models are here highlighted by means of a later,theparasiticeffectsofthetwovia-holesinlayoutregion simpleapplicationexample. (II)areaccountedforseparatelythroughastandaloneEMsim- ulationoftheviastructure.Thischoiceistwiceuseful.Infact, theFW-EManalysisoftheremaininglayoutisstronglysimpli- II. IDENTIFICATIONOF ALUMPEDPARASITICNETWORK fiedandthevia-holesmayberemovedwhenthespecificdesign THROUGHFW-EMANALYSIS applicationrequiresfloatingsourceelectrodes. Let us considerthe problem ofmodeling the extrinsicpara- Theelements , , ,and describetheseriespara- siticphenomenaassociatedwiththetypicaldevicelayoutshown siticeffectsduetothemultigate/drain-fingerlayoutregion(IV). inFig.1throughascalablelumpedcomponentnetwork.Theac- Theelements , , , , ,and cessstructurestothedevice, suchas,forinstance,coplanarto (whereMdenotesmetallization)accountforthecapacitive-like microstrip line transitions, are considered apart in this context coupling and dielectric losses both between the metallization (suitable instrument calibration procedures may be adopted in structures of the gate and drain fingers and between the gate/ ordertosetthedevicecharacterizationsectionsattheexternal drain fingers and the air bridge. It is worth noting that since edgesofthegateanddrainmanifolds). no doped layers are considered in the substrate definition for In addition, parasitic phenomena associated with doped theEMsimulations,theevaluationof and isto- layersinthesemiconductorsubstratearenottakenintoaccount tally unaffected by the gate–source and gate–drain barrier ca- here (a simple homogeneous substrate is assumed in the EM pacitancesassociatedwiththemobilechargedepletionbeneath simulations of the device layout). Thus, additional modeling theSchottkygateinactualdevices. RESCAetal.:SCALABLEEQUIVALENTCIRCUITFETMODELFORMMICDESIGNIDENTIFIEDTHROUGHFW-EMANALYSES 247 A. ModelScalingRules TABLEI LCMODELOFTHEGATEANDDRAINMANIFOLDS Let us first define geometry-dependent scaling factors [20] such as (1) where , , , and are the gatewidth and the number of gate fingers of the scaled and reference device, re- spectively. According to the axes reference system shown in Fig.1,thesubscript“ ”representsthedirectionalongthegate/ drainfingers( -axis),while“ ”denotesthedirectionalongthe channel( -axis),respectively.Thus,thefactors and willbeappliedwheneverascalingofthegatewidthand/oradif- ferentnumberofparalleledfingersareinvolved. We first consider the parasitic phenomena associated to the layoutregion(IV).Simplescalingrulesaredefinedinthiscase forthelumpedcomponentsofthecorrespondingschematicre- gion.Theserulesstatethat[20] (2) (3) Fig.3. Variationofthe(cid:0),(cid:2)parametersinthegateanddrainmanifoldmodels More interesting considerations concern layout region (I). withthenumberofgatefingers:(cid:0) (triangles),(cid:0) (crosses),(cid:2) (cid:0)(cid:2) Thegateanddrainmanifoldswidening(orshrinkage)effectsin (circles),(cid:2) (cid:0)(cid:2) (squares).(cid:0)(cid:2) isevaluatedbyconsideringsixgatefingers inthereferencedevice. thepresenceofavaryingnumber offingersareinvestigated herethroughsimpleEMsimulations.Tothisaim,thegateand drain manifold layouts of the generic device are easily drown fingers ( evaluated by considering six gate fingers in the by modifying the reference device layout on the basis of the referencedevice). minimum distance along the -axis between two successive Theobtainedresultsjustifythefollowingscalingrulesforthe gate fingers. The study is carried out for a number of fingers parasiticlumpedcomponentsinschematicregion(I) rangingfrom4to12,whichcorrespondstothesetofelectron devicesmadeavailableinthefoundryprocessconsidered. The EM simulation of each gate manifold is carried out by (4) placing -ports,onefortheconnectiontotheexternalgate lineandonefortheconnectiontoeachinternalgatefinger[22] We consider now the parasitic phenomena associated to (only “gap ports” are used since they are exactly deembedded layout regions (II) and (III). At first glance, and could bytheEMsolver[23],[24]).Sinceourgoalisthedefinitionofa be considered analogous to the corresponding gate or drain lumpedcomponentscalabledescriptionoftheparasiticeffects components,butrelatedtothemodelingoftheparasiticeffects associated to the manifold, the internal ports are then short associated to the source fingers. According to this view [20], circuitedleadingtoatwo-portEM-baseddescriptionofthegate and should be scaled by using the same rules (2) used manifold. A simple LC network, as shown in gate region (I) forthegateanddrainseriesparasiticeffects. of Fig. 2 perfectly fits the obtained two-port description up to However,inthisparticularcase,amoreappropriateanalysis 100 GHz. ofthedevicelayoutshouldalsotakeintoaccountthepresenceof Thesameprocedureisappliedalsotothedrainmanifold,with theairbridge,asshowninFig.4.Inoppositiontotheprevious theonlydifferencethat internalportsareconsideredsince point of view, this structure suggests that and should thedrainfingersarehalfthenumberofgatefingers. not scale with the device periphery. In fact, since the internal TheextractedvaluesoftheLCmodelparametersconcerning sourcefingersareconnectedtothegroundterminalthroughthe thegateanddrainmanifoldsareshowninTableI.Itisobserved air bridge, which is running along the -axis, negligible para- thatthevaluesof and arenearlyconstantversusthe sitic effects actually take place in the -direction (the source numberoffingers,whilethevaluesof and increase fingeroppositeendsalmostcorrespondtoopenimpedanceter- almost linearly with , according to the scaling factor . minations). This is also clearly seen in Fig. 3, where the extracted induc- Theseriesparasiticphenomenaassociatedwiththeairbridge tancesandscaledcapacitancesareplottedversusthenumberof along the -axis can be considered almost negligible with re- 248 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 Fig.4. Crosssectionoftheairbridgeprovidinggroundconnectiontothein- ternalsourcefingers(sixgatefingerdevice).Theentireextrinsicstructureas- sociatedwiththesourceiscomposedbythevia-holesinlayoutregion(II)con- nectedtotheairbridgerepresentinglayoutregion(III)(seeFig.1). spect to those introduced by the via-holes, as confirmed by a dedicatedEManalysisoftheair-bridgestandalone. Thus,sincethevia-holes(actuallytwoviasconnectedinpar- allel)arethesameforallthedeviceperipheries,the and elementsofFig.2maybethoughtofnotrequiringanyscaling at all, i.e., (5) Particularcaremustbepaidwhenthesourcestructureisei- therdifferentthanthatofFig.4ortheairbridgehassignificant parasiticeffectssincethesourceparasiticelementsscalingrule (5)mightchange. B. ModelIdentification The identification of the extrinsic lumped components is based on a few FW-EM simulations of a single reference Fig.5. Flowchartdescribingthemodelextractionprocedure.TheFW-EMsim- device structure. Measurements under off-state conditions [or ulationsEM1,EM2,andEM3aredescribedinSectionII-B. forward-gatecoldfield-effecttransistor(FET)]andcharacteri- zationofmultipledifferent-in-sizedevicesarenotrequiredfor TABLEII theidentificationoftheextrinsicelementsusingourapproach. EXTRACTEDPARASITICPARAMETERS TheFW-EManalysesneedofcoursetheknowledgeofthesub- strate physical constants and the geometry of the metal layers oftheFET[18],[20].Thesedataareusuallyprovidedwiththe foundry design kit of any technological process (GDSII files defining the device layout are for instance needed along with informationaboutthethicknessofmetallayers). Acommercial3-DplanarEMsolver[23],providingaccurate calibrationalgorithmsforthedeembeddingofportsdiscontinu- Adistributedtwo-portdescriptionassociatedtotheentireex- ities[24],isadoptedanda6 50 mpHEMT m trinsiclayoutisthenobtainedbyconnectingthesource-portsof isselectedasthereferencedeviceinthisstudy. network EM1 to the description EM2 of the via-holes. This is AccordingtotheflowchartshowninFig.5,themodeliden- finally used (by means of a standard optimization routine) for tificationprocedureconsistsofthreedifferentsteps. theidentificationoftheremainingextrinsiccircuitparameters: EM simulations of the reference device are performed in , and , . step (i). They are: EM1) the FW-EM analysis of the four-port Theextractionprocedureoftheextrinsicelementsinvolvesa device extrinsic structure (four calibrated ports [24] are used: very well-conditioned optimization problem in ten unknowns. port-1 for the gate, port-2 for the drain, and ports 3–4 for the Fast convergence to the same solution is observed by consid- two source electrodes); EM2) the FW-EM simulation of the ering very different initial guesses of the parameter values. In conic via-hole; and EM3) the FW-EM simulations of the gate some cases, residual parasitic contributions deriving from the anddrainmanifolds. sourcefingerscouldbeeffectivelyconsideredintheoptimiza- In step (ii), the simulated data are used in order to extract tion. theextrinsicECPs.First,RSandLSinregion(II)and(III)are Finally, the measured behavior of the reference device is extracted by fitting the via-hole simulation EM2, while , deembedded from the extracted extrinsic equivalent circuit in , ,and inregion(I)areextractedbyfittingthe step (iii). The obtained description is eventually used for the gateanddrainmanifoldsimulationsEM3. identificationofthepreferredintrinsicdevicemodel. RESCAetal.:SCALABLEEQUIVALENTCIRCUITFETMODELFORMMICDESIGNIDENTIFIEDTHROUGHFW-EMANALYSES 249 Fig.6. MAG(orMSGwhereMAGisundefined)andthestabilityfactor(cid:0)versusfrequency.(a)6(cid:0)50(cid:0)m.(b)10(cid:0)50(cid:0)m.(c)10(cid:0)60(cid:0)m.(d)12(cid:0)75(cid:0)m pHEMTs.Measurements(circles)versuspredictionsobtainedthroughdifferentscalablemodels:proposedmodel(boldlines),modelpresentedin[20](lines), andmodelprovidedbythefoundry(dots).Theresultsrefertothedevicesbiasedintypicalclass-Aoperation.Analogousresultsareobtainedindifferentbias conditions. Thus,asinglesetof -parametermeasurementsattheoper- device.Thus,thelineartable-baseddescriptionoftheintrinsic ating bias on a single device periphery is only needed for the device, in terms of admittance matrix, is used hereinafter in identificationofourlinearscalablemodel. conjunction with simple linear rules for the scaling of the intrinsicdevicebehavior(i.e., ). III. EXPERIMENTALVALIDATIONOFTHESCALABLEMODEL The complete linear scalable model is now experimentally Experimentalvalidationoftheproposedmodelingapproach validated in terms of prediction capabilities of both -param- is here provided by means of a family of 0.25- m GaAs eters and global design parameters such as the stability factor pHEMTs.Thechosenreferencedeviceisa6 50 mpHEMT. [21], the MAG or the maximum stable gain (MSG), when- FW-EMsimulationsareperformedinthefrequencyrangeof evertheMAGisnotdefined[2].Thisrepresentsaratherheavy 0–100 GHz. The extracted values of the gate and drain mani- experimentalvalidationsinceitalsotakesintoaccounttheway folds parasitic elements have already been reported in Table I thediscrepanciesinthepredictionofeach -parametercombine forthesix-fingerreferencedevice.Theoptimizationsinvolved withinsuchimportantglobalfiguresofmerit. intheidentificationprocedureoutlinedinSectionII-Barecar- Four devices are considered, having remarkable differences ried out in order to fit the EM simulation data up to the max- innumberofgatefingersandgatewidth,namely,the6 50 m imumsimulatedfrequencyof100GHz.Theextractedvaluesof pHEMTreferencedeviceplusa10 50 m,a10 60 mand theparasiticelementsarelistedinTableII. a12 75 mpHEMTs. -parameter measurements in the frequency range ScaledmodelresultsareplottedinFigs.6and7.Predictions (5–65GHz)areperformedbiasingthedeviceat V, arecomparedbothtothescalablemodeldescribedin[20]and V mA , which corresponds to the typical the linear scalable foundry model. It must be pointed out that condition for the design of a power amplifier (PA) working in thefoundrydesignkitdoesnotprovideasinglescalablemodel, class-Aoperation. but different linear scalable models, each one extracted for a Following the identification procedure described in givennumberoffingers;thus,thefingerwidthistheonly“true” Section II-B, the measurements are deembedded from the scalingvariableavailable.Thefoundrymodelsarerelatedtothe parasitic elements in order to obtain the intrinsic measured operating bias condition V and mA/mm admittance parameters. These data can be used for the iden- (whichcorrespondstothescaledclass-Aoperatingconditionof tification of any intrinsic linear (or nonlinear) device model. our6 50 mreferencedevice). However,since the aim of this study is to investigate the scal- Accuracyimprovementswithrespecttothemodelpresented ability of the proposed extrinsic parasitic modeling approach, in[20]areevidentfromFigs.6and7.Thisisduetothemod- we prefer to avoid using any particular model for the intrinsic ified scaling rules and the improved extraction procedure pro- 250 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 Fig.8. MAGversusnumberofgatefingersandfingerwidthsat30GHzevalu- atedthroughtheproposedmodel.TheblackdotsaretheMAGvaluesmeasured onactualdevicesamples.Boldlineshighlightthedifferencesbetweenmeasured andsimulatedvalues. easilyscalablewithrespecttotheunitgatewidthonlysincedata ofdifferentEMsimulationsarerequiredtomodelthechangein the number of fingers. For this reason, the number of fingers cannotbeusedassweptoroptimizationvariable. TheexperimentalresultsinFigs.6and7highlightthepredic- tionaccuracyoftheproposedscalablemodelforawidesetof deviceswithinthetechnologicalprocessundertest.Thisleads the quite interesting opportunity of evaluating the way typical designparametersvaryasafunctionoflayoutparameters,such asthenumber ofgatefingersandthegatewidth .Itisim- portantto notice thatthis task cannot always be accomplished bysimplysweepingsuitablescalingvariables.Forexample,the providedfoundrymodelnecessarilyinvolvesaseparatesimula- tionforeachdifferentnumberofgatefingers. TheMAGisshown,forinstance,inFig.8,with ranging from4to12,and from30to100 m.Theseresults,which have been obtained by simply, continuously sweeping the scalingvariables,areingoodagreementwithqualitativeexpec- tations [1], i.e., the simulated MAG is nearly constant versus Fig.7. (cid:0)-parametersversusfrequencyforthe6(cid:0)50(cid:2)m:(a)referencedevice the number of fingers at fixedgatewidth, while it decreases as andthelargest(cid:0)12(cid:0)75(cid:2)m(cid:2)(b)scaleddevice.Measurements(circles)versus thedevicegatewidthincreases. predictionsobtainedthroughdifferentscalablemodels:proposedmodel(bold lines),model[20](lines),andfoundrymodel(dots).Theresultsrefertothe Thesameexperimenthasbeenrepeatedbyusingthescalable devicebiasedintypicalclass-Aoperation. foundrymodelinvolvingaseparatesimulationforeachdifferent numberofgatefingers.Thecorrespondingresultsareshownin Fig.9. posedinthispaper.Inaddition,experimentalresultsinFigs.6 Predicted and actual measured values of the MAG for the and7pointoutthatthenewscalablemodelisatleastasaccu- available device sizes are reported in Table III. The results rateasthemostadvancedfoundrylinearscalablemodels.This quantitativelyshowthattheproposedmodelaccuratelypredicts isaninterestingresultconsideringthattheproposedmodelhas (even slightly better than foundry model) the gain variations beenobtainedbyexploitingtheminimumamountofEMsimu- with respect to the unit gatewidth. Deviations reported in lateddataandasinglesetof -parametermeasurementscarried TableIIIarealsographicallyhighlightedinFigs.8and9. outforasinglereferencedeviceattherequiredoperatingcon- Theresultspresentedinthissectionshowthatalumpedrep- dition.Onthecontrary,thefoundrymodelisextractedbyusing resentation of the extrinsic parasitic phenomena, identified by bothEMsimulations,aswellasadditionalmeasurementsper- meansofsuitableEMsimulations,leadtoaanaccuratescalable formedondifferent-in-sizedevices,evenconsideringbiascon- modelcoveringallthepossibledevicesizesactuallymanufac- ditions different with respect to the operating one. More pre- turedbythefoundry. cisely,EM-baseddatamatricesareusedforthemodelingofthe access structures, while the additional measurements are used IV. EXAMPLEOFOPTIMUMPERIPHERYSELECTION inordertoextracttheparasiticelementsatthefingerregionref- erence planes (mixed physical–empirical scaling rules are de- Apracticalexploitationexampleoftheadvantagesprovided rivedatthesereferenceplanes).Thefoundrymodelis,therefore, by the proposed scalable modeling approach is provided here. RESCAetal.:SCALABLEEQUIVALENTCIRCUITFETMODELFORMMICDESIGNIDENTIFIEDTHROUGHFW-EMANALYSES 251 Fig.9. MAGversusnumberofgatefingersandfingerwidthsat30GHzeval- Fig.10. Stabilityfactor(cid:0)versusnumberofgatefingersandfingerwidthsat uatedthroughthefoundrymodel.TheblackdotsaretheMAGvaluesmeasured 30GHzevaluatedthroughtheproposedmodel.Thegrayplanecorrespondsto onactualdevicesamples.Boldlineshighlightthedifferencesbetweenmeasured the(cid:0) (cid:0) (cid:2)threshold. andsimulatedvalues. TABLEIII MEASUREDVERSUSMODELEDMAG@30GHz Let us consider the goal of selecting the optimum device pe- riphery for the design of a narrowband linear driver amplifier workingat30GHz. Differentcriteriacanbeadoptedforthechoiceoftheelemen- Fig.11. Loadandsourcereflectioncoefficients((cid:3) and(cid:3) )providinginput/ tarydevicecelltobeparalleledinordertoachievetherequired outputsimultaneousconjugatematchversusnumberofgatefingersandfinger widths((cid:0)and(cid:2))at30GHz.(cid:0)varyingfrom4to12numberoffingers(even outputpower.Afirstselectioncouldbebasedonthemaximiza- numbers),(cid:2) varyingfrom30to100(cid:3)m,step5(cid:3)m.Thearrowsshowhowthe tionofMAG,whensimultaneousinput/outputconjugatematch reflectioncoefficientsvarywhentheindependentvariablesincrease. (SCM) conditions are satisfied [2]. On the other hand, termi- nating impedances providing SCM can be only considered if thetransistorisunconditionallystableatthedesiredfrequency. V. CONCLUSION Inordertotestthiscondition,thestabilityfactor isevaluated Anewscalablemodelingapproachhasbeenpresentedinthis versusthedeviceperipherybyconsidering paper.Itisbasedonthedefinitionofalumpedcomponentde- and m.Tothisaim,trivial -param- scriptionoftheextrinsicparasiticnetwork,whichisprovento etersimulationsareautomaticallyrepeatedbysweepingthe be perfectly scalable with the number of gate fingers and the and variables.CorrespondingresultsarepresentedinFig.10, corresponding finger width. The device scalable parasitic ele- showing that most of the investigated peripheries are in this ments are identified by using only EM simulation data of just caseunconditionallystableat30GHz.Analogously,sourceand onereferencedevice.Thismeansthatneitherdevicemeasure- loadreflectioncoefficients( and ),providinginput/output mentsinconvenientconditionsofpassivity(i.e.,pinched-offor SCMconditions,areplottedontheSmithChartversus and forward-gatecoldFETconditions),nordifferent-in-sizedevice in Fig. 11. Optimum periphery selection can be easily car- measurementsarerequiredfortheextrinsicelementextraction. riedoutonthebasisoftheseresults,according tosuitable de- Theextrinsicequivalentcircuitelementsarecorrectlylinked signconstraintssuchasgain,sensitivitytoparametervariations, to the device layout, allowing the model to scale with simple physicalfeasibilityofthematchingnetworks,stabilitymargin, linear rules related to geometric-based scaling factors. Such and so on. scaling rules are process independent since they are neither The results shown in Figs. 8, 10, and 11 are easily and im- completely empirical, nor fitting based. Besides its simple mediately obtained by means of the proposed model. Instead, definition and identification procedure, the proposed scalable the same investigation would require separate sets of simula- model provide good accuracy in the prediction of different tions(oneforeachdifferentnumberofgatefingers),whenusing deviceshavingdifferentperipheries. the foundry model. This limitation could become dramatic if Finally,theproposedmodelallowsthedesignertousethede- more complex optimization problems involving and as vicegeometricalparameters(inthiscase,thenumberoffingers unknownparameterswereconsidered. andunitgatewidth)assweptandoptimizationvariables.

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272 Pages·2009·27.199 MB·English
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FEBRUARY2009 VOLUME57 NUMBER2 IETMAB (ISSN0018-9480) PAPERS LinearandNonlinearDeviceModeling ScalableEquivalentCircuitFETModelforMMICDesignIdentifiedThroughFW-EMAnalyses.......................... ................................................................. D.Resca,A.Raffo,A.Santarelli,G.Vannini,andF.Filicori 245 AnalyticalExtractionofExtrinsicandIntrinsicFETParameters ....................B.L. Ooi,Z.Zhong,andM.-S.Leong 254 AComprehensiveAnalysisofAM–AMandAM–PMConversioninanLDMOSRFPowerAmplifier.................... ...................................................................................................... J.P.AikioandT.Rahkonen 262 ABroadbandandScalableLossySubstrateModelforRFNoiseSimulationandAnalysisinNanoscaleMOSFETsWith VariousPadStructures .............................................................................. J.-C.GuoandY.-H.Tsai 271 ANonlinearElectro-ThermalScalableModelforHigh-PowerRFLDMOSTransistors..................................... ................................ J.Wood,P.H.Aaen,D.Bridges,D.Lamey,M.Guyonnet,D.S.Chan,andN.Monsauret 282 SmartAntennas,PhasedArrays,andRadars ACircularlyPolarizedBalancedRadarFront-EndWithaSingleAntennafor24-GHzRadarApplications ............... ................................................................................... C.-Y.Kim,J.-G.Kim,D.Baek,andS.Hong 293 ActiveCircuits,SemiconductorDevices,andICs DesignandAnalysisfora60-GHzLow-NoiseAmplifierWithRFESDProtection .......................................... ................................... B.-J.Huang,C.-H.Wang,C.-C.Chen,M.-F.Lei,P.-C.Huang,K.-Y.Lin,andH.Wang 298 A50–300-MHzHighlyLinearandLow-NoiseCMOS - FilterAdoptingMultipleGatedTransistorsforDigitalTV TunerICs......................................................................................K.Kwon,H.-T.Kim,andK.Lee 306 Optimizing Losses in Distributed Multiharmonic Matching Networks Applied to the Design of an RF GaN Power AmplifierWithHigherThan80%Power-AddedEfficiency.......................... M. HelaouiandF.M.Ghannouchi 314 DigitalBasebandPredistortionBasedLinearizedBroadbandInverseClass-EPowerAmplifier ............................ ............................................................................................. M.Thian,M.Xiao,andP.Gardner 323 0.5-V5.6-GHzCMOSReceiverSubsystem .................... H.-C.Chen,T.Wang,H.-W.Chiu,T.-H.Kao,andS.-S.Lu 329 The Effects of Limited Drain Current and On Resistance on the Performance of an LDMOS Inverse Class-E Power Amplifier .................................................................................. F.You,S.He,X.Tang,andX.Deng 336 (ContentsContinuedonBackCover) (ContentsContinuedfromFrontCover) SignalGeneration,FrequencyConversion,andControl LowPhaseNoiseSelf-SwitchedBiasingCMOSLCQuadratureVCO ............................ G.HuangandB.-S.Kim 344 FieldAnalysisandGuidedWaves HighlyEfficientGroupingStrategyfortheAnalysisofTwo-PortArbitrarilyShaped -PlaneWaveguideDevices ...... ..........................Á.BelenguerMartínez,H.EstebanGonzález,V.E.BoriaEsbert,C.Bachiller,andJ.V.Morro 352 CADAlgorithmsandNumericalTechniques BroadbandModelingofHigh-FrequencyMicrowaveDevices........D.Paul,M.S.Nakhla,R.Achar,andA.Weisshaar 361 SurfaceInteractionMatricesforBoundaryIntegralAnalysisofLossyTransmissionLines ................................. .................................................................................................. A.SiripuramandV.Jandhyala 374 AcceleratedMicrowaveDesignOptimizationWithTuningSpaceMapping .................................................. .............................................................. S.Koziel,J.Meng,J.W.Bandler,M.H.Bakr,andQ.S.Cheng 383 An Efficient Perturbative Approach for Finite-Element Analysis of Microwave Devices Exhibiting Small Geometrical Variations .................................................................. G. Guarnieri,G.Pelosi,L.Rossi,andS.Selleri 395 WaveguideMicrowaveImaging:NeuralNetworkReconstructionofFunctional2-DPermittivityProfiles................. ................................................................................ A.V.Brovko,E.K.Murphy,andV.V.Yakovlev 406 EfficientAlgorithmforPassivityEnforcementof -Parameter-BasedMacromodels......................................... ..................................................................................... T.Dhaene,D.Deschrijver,andN.Stevens 415 AMultiple-LineDoubleMultirateShootingTechniquefortheSimulationofHeterogeneousRFCircuits................. .................................................................................................... J.F.OliveiraandJ.C.Pedro 421 FiltersandMultiplexers ApplicationofRepresentationTheorytoDual-ModeMicrowaveBandpassFilters ................................ S.Amari 430 Packaging,Interconnects,MCMs,Hybrids,andPassiveCircuitElements Wire-BondFreeTechniqueforRight-AngleCoplanarWaveguideBendStructures .... H.KimandR.Franklin-Drayton 442 AnalyticalSolutionforVoltage-StepResponseofLossyDistributedRCLines ................ A. PunningandE.Jalviste 449 InstrumentationandMeasurementTechniques NoninvasiveProcedureforMeasuringtheComplexPermittivityofResins,Catalysts,andOtherLiquidsUsingaPartially FilledRectangularWaveguideStructure ........................................M.J. Akhtar,L.E.Feher,andM.Thumm 458 ABroadbandandStableMethodforUniqueComplexPermittivityDeterminationofLow-LossMaterials................ ................................................................................................. U.C.HasarandC.R.Westgate 471 Microwave Photonics SpaceMappingWithAdaptiveResponseCorrectionforMicrowaveDesignOptimization .................................. ........................................................................................ S.Koziel,J.W.Bandler,andK.Madsen 478 AnInvestigationoftheOperationandPerformanceofCoherentMicrowavePhotonicFilters............................... ...................................................................................................... B.C.PileandG.W.Taylor 487 ChirpedMicrowavePulseCompressionUsingaPhotonicMicrowaveFilterWithaNonlinearPhaseResponse .......... ............................................................................................................... C.WangandJ.Yao 496 MicrowaveFrequencyMeasurementBasedonOpticalPowerMonitoringUsingaComplementaryOpticalFilterPair .. ....................................................................................................... X.Zou,H.Chi,andJ.Yao 505 InformationforAuthors ............................................................................................................ 512 IEEEMICROWAVETHEORYANDTECHNIQUESSOCIETY TheMicrowaveTheoryandTechniquesSocietyisanorganization,withintheframeworkoftheIEEE,ofmemberswithprincipalprofessionalinterestsinthefieldofmicrowavetheory andtechniques.AllmembersoftheIEEEareeligibleformembershipintheSocietyuponpaymentoftheannualSocietymembershipfeeof$14.00,plusanannualsubscriptionfee of$23.00peryearforelectronicmediaonlyor$46.00peryearforelectronicandprintmedia.Forinformationonjoining,writetotheIEEEattheaddressbelow.Membercopiesof Transactions/Journalsareforpersonaluseonly. ADMINISTRATIVECOMMITTEE B.PERLMAN, President S.M.EL-GHAZALY PresidentElect W.CHAPPELL, Secretary N.KOLIAS, Treasurer L.BOGLIONI M.HARRIS L.KATEHI J.LIN V.J.NAIR D.ROSEN W.SHIROMA B.SZENDRENYI R.WEIGEL M.GUPTA J.HAUSNER B.KIM A.MORTAZAWI Y.NIKAWA D.SCHREURS R.SNYDER K.VARIAN K.WU J.HACKER K.ITOH T.LEE HonoraryLifeMembers DistinguishedLecturers PastPresidents T.ITOH T.S.SAAD K.TOMIYASU G.BOECK B.KIM V.NAIR P.SIEGEL J.MODELSKI(2008) A.A.OLINER P.STAECKER L.YOUNG A.HAJIMIRI V.LUBECKE J.C.RAUTIO R.SNYDER J.S.KENNEY(2007) W.HOEFER L.MAURER D.ROOT A.SUAREZ K.VARIAN(2006) MTT-SChapterChairs Albuquerque:L.H.BOWEN Foothill:C.ANTONIAK NorthJersey:H.DARAL/K.DIXIT SouthAfrica:P.W.VANDERWALT Atlanta: D.KOKOTOFF France:P.EUDELINE NorthQueensland: M.V.JACOB SouthAustralia:B.BATES Austria:A.SPRINGER Germany:W.HEINRICH NorthernNevada: B.S.RAWAT SouthBrazil:L.C.KRETLY Baltimore:N.BUSHYAGER Greece:I.XANTHAKIS Norway:U.HANKE SoutheasternMichigan: L.M.ANNEBERG Beijing:Z.FENG HongKong:W.Y.TAM OrangeCounty:H.J.DELOSSANTOS SouthernAlberta:S.BOUMAIZA Beijing,Nanjing:W.X.ZHANG Houston:J.T.WILLIAMS Oregon:T.RUTTAN Spain:L.FEHARO Belarus: A.GUSINSKY Houston,CollegeStation: C.MADSEN Orlando: X.GONG Springfield:P.R.SIQUEIRA Benelux: D.V.-JANVIER Hungary:T.BERCELI Ottawa: Q.YE Sweden: A.RYDBERG Brasilia: A.KLAUTAU,JR. 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Montreal:K.WU Seattle:W.P.HALL VirginiaMountain:T.WINSLOW Denver:M.JANEZIC NewHampshire:T.PERKINS SeoulCouncil:H.-Y.LEE WashingtonDC/NorthernVirginia: EasternNo.Carolina:D.PALMER NewJerseyCoast:D.REYNOLDS SerbiaMontenegro: B.MILOVANOVIC B.LEVINE Egypt: I.A.SALEM NewSouthWales:G.TOWN Siberia,Novosibirsk: V.SHUBALOV Winnipeg: V.OKHMATOVSKI Finland:A.LUUKANEN NewZealand:J.MAZIERSKA Siberia,Tomsk:R.V.MESCHERIAKOV Youngnam/Taegu:Y.-H.JEONG FloridaWestCoast:K.O’CONNOR NorthItaly:G.GHIONE Singapore: A.ALPHONES Editors-In-Chief AssociateEditors DYLAN WILLIAMS DANIEL DE ZUTTER JEN-TSAI KUO MAURO MONGIARDO RICHARD SNYDER NIST Universiteit Gent Nat.ChiaoTungUniv. Univ. of Perugia RSMicrowaveCompany Boulder,CO80305USA Belgium Taiwan Italy USA Phone:+13034973138 email:[email protected] email:[email protected] email:[email protected] email:[email protected] Fax:+13034973970 email:[email protected] WOLFGANG HEINRICH YOUNGWOOKWON JOSÉ PEDRO CHI WANG Ferdinand-Braun-Institut(FBH) Seoul Nat. Univ. Univ. of Aveiro OrbitalSciencesCorp. AMIRMORTAZAWI Germany Korea Portugal USA Univ. of Michigan email:[email protected] email:[email protected] email:jcp.mtted.av.it.pt email:[email protected] AnnArbor,MI48109-2122USA Phone:+17349362597 WEI HONG JENSHAN LIN ZOYA POPOVIC KE-LI WU Fax:+17346472106 Southeast Univ. Univ. of Florida Univ.ofColorado,Boulder ChineseUniv.ofHongKong email:[email protected] China USA USA Hong Kong email:[email protected] email:[email protected] email:[email protected] email:[email protected] ROBERT W. 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DigitalObjectIdentifier10.1109/TMTT.2009.2014682 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 245 Scalable Equivalent Circuit FET Model for MMIC Design Identified Through FW-EM Analyses Davide Resca, Member, IEEE, Antonio Raffo, Member, IEEE, Alberto Santarelli, Member, IEEE, GiorgioVannini, Member, IEEE, and FabioFilicori Abstract—A scalable approach to the modeling of millimeter- gatefingers)forthespecificapplicationthroughtheevaluation wavefield-effecttransistorsispresentedinthispaper.Thisisbased ofsuitablydefinedfiguresofmeritanddesigncriteria[1],[2]. on the definition of a lumped extrinsic parasitic network, easily Scalablemodelsalsoallowforimportanttimesavingduringthe scalablewithboththenumberoffingersandthefingerwidths.The empiricalcharacterizationoffoundryprocesses. identificationoftheextrinsicnetworkparametersiscarriedoutby meansofaccuratefull-waveelectromagneticsimulationsbasedon Linear scaling rules are widely adopted for the intrinsic de- thelayoutofasinglereferencedevice. vice, providing accurate prediction results [3] up to relatively Inthepaper,theparasiticeffectsofthegate/drainmanifoldsand high frequencies. However, when microwave and millimeter- of the source layout are investigated, leading to the definition of wave applications are involved, the overall quality of an elec- realisticlinearscalingrules. tron device model also strongly depends on the rules applied The obtained model is experimentally validated by using a familyof0.25- mmillimeter-waveGaAspseudomorphicHEMTs tothescalingoftheextrinsicnetwork,describingtheparasitic throughtheaccuratepredictionofcriticalperformanceindicators, phenomena taking part in the physical interconnections of the suchasthelinearmaximumpowergainorthestabilityfactor. intrinsicdevicetotheexternallyaccessibleterminals. Despitethesimplicityoftheproposedmodel,itprovestobeas Simple linear scaling rules [4], [5] applied to conventional accurateastypicalscalablemodelsprovidedbyfoundries. lumped parasitic networks do not lead to accurate scalable Straightforwardapplicationofthescalablemodelingapproach to the optimum device geometry selection in a typical design models at high frequencies. Complex, technology-dependent problemisalsopresented. scalingrules[6]–[9]orquasi-distributedmodels[10]–[19]have beenrecentlyproposedintheliteratureinordertoimprovethe IndexTerms—Electromagnetic(EM)analysis,field-effecttran- high-frequencypredictionaccuracyofscaleddevicemodels. sistors(FETs),microwaveandmillimeter-waveintegratedcircuits (MMICs),semiconductordevicemodeling. Commercialfull-waveelectromagnetic(FW-EM)simulators have been also recently exploited (e.g., see [18] and [19]) for theanalysisofextrinsicparasiticphenomenaandthedefinition I. INTRODUCTION ofdistributedmodelingapproaches,wheretheentireactivearea isdividedintoasuitablenumberofelementary“activeslices.” Suchmodelingapproacheshavebeenprovenverysuitable for M ICROWAVE AND millimeter-wave integrated circuit scaling, providing extremely accurate electrical response pre- (MMIC) design requires empirical models, which ac- dictions. Unfortunately, their exploitation in conjunction with curately describethelinearand nonlinearbehavior ofelectron nonlinearmodelsoftheactiveslicesleadstorelativelypoornu- devicesuptoextremelyhighfrequencies.Whenembeddedinto mericalefficiencyinharmonicbalance(HB)analysesduetothe circuit schematics, accurate device models allow engineers to proliferationinthenumberofinternalnonlinearports. design and optimize the circuit performance before the actual In this paper, an almost conventional lumped parasitic net- fabrication. work is adopted. However, a new simple parameter identifica- Optimum device periphery selection in actual design tasks tionprocedureisproposedonthebasisofanFW-EMsimulation oftenrequiresadifferentmodelforeachparticulardevicelayout ofthedevicelayout.Inaddition,suitablerulesareprovidedfor inagiventechnologicalprocess.Inordertoavoidthisproblem, improvedpredictionaccuracyofscaleddevices.Typicaldevice empiricalscalablemodelsareavailableallowingthedesignerto geometricalparameters, suchasthenumberoffingersandthe selecttheoptimumdevicegeometry(i.e.,numberandwidthof unitgatewidth,maybeusedbythedesignerassweptandeven optimizationvariablesbymeansoftheproposedapproach.Al- ManuscriptreceivedApril26,2008;revisedSeptember23,2008.Firstpub- though this paper deals with linear models, the proposed ap- lishedJanuary19,2009;currentversionpublishedFebruary06,2009.Thiswork proach is totally suitable for the application of scalable non- wassupportedinpartbytheItalianMinistryofUniversityandResearch(MUR). linearmodelstotheintrinsicdevice. D. Resca, A. Santarelli, and F. Filicori are with the Department of Elec- tronics, Computer Sciences and Systems, University of Bologna, 40136 This paper is organized as follows. The proposed lumped Bologna, Italy (e-mail: [email protected]; [email protected]; parasitic network is introduced in Section II-A and the cor- ffi[email protected]). responding scaling rules are also discussed. With respect to A.RaffoandG.VanniniarewiththeDepartmentofElectronics,University of Ferrara, 44100 Ferrara, Italy (e-mail: [email protected]; giorgio.van- the somehow similar approach presented in [20], the effects [email protected]). of widening (or shrinking) of the gate and drain manifolds in Colorversionsofoneormoreofthefiguresinthispaperareavailableonline thepresenceofahigher(orlower)numberoffingersaretaken athttp://ieeexplore.ieee.org. DigitalObjectIdentifier10.1109/TMTT.2008.2011208 into account here and a new scaling rules are provided for the 0018-9480/$25.00©2009IEEE 246 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 Fig.2. Lumpedcomponentnetworkdescribingthedeviceextrinsicparasitic phenomena.Schematicregions(I)–(IV)arestrictlyrelatedtothecorresponding Fig.1. Deviceparasiticeffectssubdivisionthroughdevicelayoutconsidera- layoutregionsshowninFig.1. tions.Gateanddrainmanifolds(I),sourcevia-holes(II),airbridge(III),and fingerregion(IV)areshown. effort could be required if parasitic phenomena are expected to strongly affect these regions. It is worth noting that, the manifold and source parasitic components. The new scaling parasitic phenomena located in the doped layers have been rulesleadtocriticalimprovementinthepredictionaccuracyof considered fully negligible in the case of the 0.25- m GaAs scaled devices. pHEMTusedinthisstudy.Experimentalvalidationprovidedin Anewprocedurefortheidentificationofthelumpedcompo- SectionIIIempiricallyconfirmsthevalidityofthisassumption. nentsoftheparasiticnetworkisthenpresentedinSectionII-B. Inordertogetproperscalingrulesofthemodel,thedevice This is based on a three-step process aimed at the separation layoutinFig.1isseparatedintofourdifferentregions.Region oftheentireequivalentcircuitparameter(ECP)setintosmaller (I) accounts for the parasitic effects due to the gate and drain groups, more easily identifiable through the fitting of simpler manifolds, which feed the signals to each finger. Region (II) FW-EMsimulations. accounts for the parasitic effects due to the via-holes, which Experimental validation of the model is proposed in provides source connections to ground. Region (III) accounts Section III. A family of 0.25- m GaAs pseudomorphic for the airbridge, which providethe ground connection tothe HEMTs (pHEMTs) is fully characterized and scaled models sourcefingersthroughthevia-holepads.Region(IV)accounts are obtained from a reference device. In order to meet the de- fortheparasiticeffectsduetotheinteractionsbetweenthefinger signerpointofview,theevaluationofthepredictionaccuracyof metallizations(i.e.,ohmiclossesalongthegateanddrainfingers thescaledmodelsiscarriedoutdirectlyonthebasisofcritical and capacitive-like couplings both between the gate and drain performance indicators, such as the maximum available gain fingers themselves and between the gate/drain fingers and the (MAG),andthestabilityfactor [21].Despitethesimplicityof airbridge). the proposed approach, improvements in accuracy are proven This somehow intuitive separation leads to the lumped ex- in comparisonswith other similarapproaches [20] and typical trinsicparasiticnetworkshowninFig.2. foundrymodels. Thefourelements , , ,and (whereMde- Finally, a practical example of optimum device periphery notesmanifold)modeltheparasiticeffectsofthelayoutregion selection by means of the proposed approach is provided in (I).Theelements and modeltheeffectsofthevia-holes Section IV. Advantages with respect to other conventional andtheairbridgeinlayoutregions(II)and(III).Asdiscussed scalable device models are here highlighted by means of a later,theparasiticeffectsofthetwovia-holesinlayoutregion simpleapplicationexample. (II)areaccountedforseparatelythroughastandaloneEMsim- ulationoftheviastructure.Thischoiceistwiceuseful.Infact, theFW-EManalysisoftheremaininglayoutisstronglysimpli- II. IDENTIFICATIONOF ALUMPEDPARASITICNETWORK fiedandthevia-holesmayberemovedwhenthespecificdesign THROUGHFW-EMANALYSIS applicationrequiresfloatingsourceelectrodes. Let us considerthe problem ofmodeling the extrinsicpara- Theelements , , ,and describetheseriespara- siticphenomenaassociatedwiththetypicaldevicelayoutshown siticeffectsduetothemultigate/drain-fingerlayoutregion(IV). inFig.1throughascalablelumpedcomponentnetwork.Theac- Theelements , , , , ,and cessstructurestothedevice, suchas,forinstance,coplanarto (whereMdenotesmetallization)accountforthecapacitive-like microstrip line transitions, are considered apart in this context coupling and dielectric losses both between the metallization (suitable instrument calibration procedures may be adopted in structures of the gate and drain fingers and between the gate/ ordertosetthedevicecharacterizationsectionsattheexternal drain fingers and the air bridge. It is worth noting that since edgesofthegateanddrainmanifolds). no doped layers are considered in the substrate definition for In addition, parasitic phenomena associated with doped theEMsimulations,theevaluationof and isto- layersinthesemiconductorsubstratearenottakenintoaccount tally unaffected by the gate–source and gate–drain barrier ca- here (a simple homogeneous substrate is assumed in the EM pacitancesassociatedwiththemobilechargedepletionbeneath simulations of the device layout). Thus, additional modeling theSchottkygateinactualdevices. RESCAetal.:SCALABLEEQUIVALENTCIRCUITFETMODELFORMMICDESIGNIDENTIFIEDTHROUGHFW-EMANALYSES 247 A. ModelScalingRules TABLEI LCMODELOFTHEGATEANDDRAINMANIFOLDS Let us first define geometry-dependent scaling factors [20] such as (1) where , , , and are the gatewidth and the number of gate fingers of the scaled and reference device, re- spectively. According to the axes reference system shown in Fig.1,thesubscript“ ”representsthedirectionalongthegate/ drainfingers( -axis),while“ ”denotesthedirectionalongthe channel( -axis),respectively.Thus,thefactors and willbeappliedwheneverascalingofthegatewidthand/oradif- ferentnumberofparalleledfingersareinvolved. We first consider the parasitic phenomena associated to the layoutregion(IV).Simplescalingrulesaredefinedinthiscase forthelumpedcomponentsofthecorrespondingschematicre- gion.Theserulesstatethat[20] (2) (3) Fig.3. Variationofthe(cid:0),(cid:2)parametersinthegateanddrainmanifoldmodels More interesting considerations concern layout region (I). withthenumberofgatefingers:(cid:0) (triangles),(cid:0) (crosses),(cid:2) (cid:0)(cid:2) Thegateanddrainmanifoldswidening(orshrinkage)effectsin (circles),(cid:2) (cid:0)(cid:2) (squares).(cid:0)(cid:2) isevaluatedbyconsideringsixgatefingers inthereferencedevice. thepresenceofavaryingnumber offingersareinvestigated herethroughsimpleEMsimulations.Tothisaim,thegateand drain manifold layouts of the generic device are easily drown fingers ( evaluated by considering six gate fingers in the by modifying the reference device layout on the basis of the referencedevice). minimum distance along the -axis between two successive Theobtainedresultsjustifythefollowingscalingrulesforthe gate fingers. The study is carried out for a number of fingers parasiticlumpedcomponentsinschematicregion(I) rangingfrom4to12,whichcorrespondstothesetofelectron devicesmadeavailableinthefoundryprocessconsidered. The EM simulation of each gate manifold is carried out by (4) placing -ports,onefortheconnectiontotheexternalgate lineandonefortheconnectiontoeachinternalgatefinger[22] We consider now the parasitic phenomena associated to (only “gap ports” are used since they are exactly deembedded layout regions (II) and (III). At first glance, and could bytheEMsolver[23],[24]).Sinceourgoalisthedefinitionofa be considered analogous to the corresponding gate or drain lumpedcomponentscalabledescriptionoftheparasiticeffects components,butrelatedtothemodelingoftheparasiticeffects associated to the manifold, the internal ports are then short associated to the source fingers. According to this view [20], circuitedleadingtoatwo-portEM-baseddescriptionofthegate and should be scaled by using the same rules (2) used manifold. A simple LC network, as shown in gate region (I) forthegateanddrainseriesparasiticeffects. of Fig. 2 perfectly fits the obtained two-port description up to However,inthisparticularcase,amoreappropriateanalysis 100 GHz. ofthedevicelayoutshouldalsotakeintoaccountthepresenceof Thesameprocedureisappliedalsotothedrainmanifold,with theairbridge,asshowninFig.4.Inoppositiontotheprevious theonlydifferencethat internalportsareconsideredsince point of view, this structure suggests that and should thedrainfingersarehalfthenumberofgatefingers. not scale with the device periphery. In fact, since the internal TheextractedvaluesoftheLCmodelparametersconcerning sourcefingersareconnectedtothegroundterminalthroughthe thegateanddrainmanifoldsareshowninTableI.Itisobserved air bridge, which is running along the -axis, negligible para- thatthevaluesof and arenearlyconstantversusthe sitic effects actually take place in the -direction (the source numberoffingers,whilethevaluesof and increase fingeroppositeendsalmostcorrespondtoopenimpedanceter- almost linearly with , according to the scaling factor . minations). This is also clearly seen in Fig. 3, where the extracted induc- Theseriesparasiticphenomenaassociatedwiththeairbridge tancesandscaledcapacitancesareplottedversusthenumberof along the -axis can be considered almost negligible with re- 248 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 Fig.4. Crosssectionoftheairbridgeprovidinggroundconnectiontothein- ternalsourcefingers(sixgatefingerdevice).Theentireextrinsicstructureas- sociatedwiththesourceiscomposedbythevia-holesinlayoutregion(II)con- nectedtotheairbridgerepresentinglayoutregion(III)(seeFig.1). spect to those introduced by the via-holes, as confirmed by a dedicatedEManalysisoftheair-bridgestandalone. Thus,sincethevia-holes(actuallytwoviasconnectedinpar- allel)arethesameforallthedeviceperipheries,the and elementsofFig.2maybethoughtofnotrequiringanyscaling at all, i.e., (5) Particularcaremustbepaidwhenthesourcestructureisei- therdifferentthanthatofFig.4ortheairbridgehassignificant parasiticeffectssincethesourceparasiticelementsscalingrule (5)mightchange. B. ModelIdentification The identification of the extrinsic lumped components is based on a few FW-EM simulations of a single reference Fig.5. Flowchartdescribingthemodelextractionprocedure.TheFW-EMsim- device structure. Measurements under off-state conditions [or ulationsEM1,EM2,andEM3aredescribedinSectionII-B. forward-gatecoldfield-effecttransistor(FET)]andcharacteri- zationofmultipledifferent-in-sizedevicesarenotrequiredfor TABLEII theidentificationoftheextrinsicelementsusingourapproach. EXTRACTEDPARASITICPARAMETERS TheFW-EManalysesneedofcoursetheknowledgeofthesub- strate physical constants and the geometry of the metal layers oftheFET[18],[20].Thesedataareusuallyprovidedwiththe foundry design kit of any technological process (GDSII files defining the device layout are for instance needed along with informationaboutthethicknessofmetallayers). Acommercial3-DplanarEMsolver[23],providingaccurate calibrationalgorithmsforthedeembeddingofportsdiscontinu- Adistributedtwo-portdescriptionassociatedtotheentireex- ities[24],isadoptedanda6 50 mpHEMT m trinsiclayoutisthenobtainedbyconnectingthesource-portsof isselectedasthereferencedeviceinthisstudy. network EM1 to the description EM2 of the via-holes. This is AccordingtotheflowchartshowninFig.5,themodeliden- finally used (by means of a standard optimization routine) for tificationprocedureconsistsofthreedifferentsteps. theidentificationoftheremainingextrinsiccircuitparameters: EM simulations of the reference device are performed in , and , . step (i). They are: EM1) the FW-EM analysis of the four-port Theextractionprocedureoftheextrinsicelementsinvolvesa device extrinsic structure (four calibrated ports [24] are used: very well-conditioned optimization problem in ten unknowns. port-1 for the gate, port-2 for the drain, and ports 3–4 for the Fast convergence to the same solution is observed by consid- two source electrodes); EM2) the FW-EM simulation of the ering very different initial guesses of the parameter values. In conic via-hole; and EM3) the FW-EM simulations of the gate some cases, residual parasitic contributions deriving from the anddrainmanifolds. sourcefingerscouldbeeffectivelyconsideredintheoptimiza- In step (ii), the simulated data are used in order to extract tion. theextrinsicECPs.First,RSandLSinregion(II)and(III)are Finally, the measured behavior of the reference device is extracted by fitting the via-hole simulation EM2, while , deembedded from the extracted extrinsic equivalent circuit in , ,and inregion(I)areextractedbyfittingthe step (iii). The obtained description is eventually used for the gateanddrainmanifoldsimulationsEM3. identificationofthepreferredintrinsicdevicemodel. RESCAetal.:SCALABLEEQUIVALENTCIRCUITFETMODELFORMMICDESIGNIDENTIFIEDTHROUGHFW-EMANALYSES 249 Fig.6. MAG(orMSGwhereMAGisundefined)andthestabilityfactor(cid:0)versusfrequency.(a)6(cid:0)50(cid:0)m.(b)10(cid:0)50(cid:0)m.(c)10(cid:0)60(cid:0)m.(d)12(cid:0)75(cid:0)m pHEMTs.Measurements(circles)versuspredictionsobtainedthroughdifferentscalablemodels:proposedmodel(boldlines),modelpresentedin[20](lines), andmodelprovidedbythefoundry(dots).Theresultsrefertothedevicesbiasedintypicalclass-Aoperation.Analogousresultsareobtainedindifferentbias conditions. Thus,asinglesetof -parametermeasurementsattheoper- device.Thus,thelineartable-baseddescriptionoftheintrinsic ating bias on a single device periphery is only needed for the device, in terms of admittance matrix, is used hereinafter in identificationofourlinearscalablemodel. conjunction with simple linear rules for the scaling of the intrinsicdevicebehavior(i.e., ). III. EXPERIMENTALVALIDATIONOFTHESCALABLEMODEL The complete linear scalable model is now experimentally Experimentalvalidationoftheproposedmodelingapproach validated in terms of prediction capabilities of both -param- is here provided by means of a family of 0.25- m GaAs eters and global design parameters such as the stability factor pHEMTs.Thechosenreferencedeviceisa6 50 mpHEMT. [21], the MAG or the maximum stable gain (MSG), when- FW-EMsimulationsareperformedinthefrequencyrangeof evertheMAGisnotdefined[2].Thisrepresentsaratherheavy 0–100 GHz. The extracted values of the gate and drain mani- experimentalvalidationsinceitalsotakesintoaccounttheway folds parasitic elements have already been reported in Table I thediscrepanciesinthepredictionofeach -parametercombine forthesix-fingerreferencedevice.Theoptimizationsinvolved withinsuchimportantglobalfiguresofmerit. intheidentificationprocedureoutlinedinSectionII-Barecar- Four devices are considered, having remarkable differences ried out in order to fit the EM simulation data up to the max- innumberofgatefingersandgatewidth,namely,the6 50 m imumsimulatedfrequencyof100GHz.Theextractedvaluesof pHEMTreferencedeviceplusa10 50 m,a10 60 mand theparasiticelementsarelistedinTableII. a12 75 mpHEMTs. -parameter measurements in the frequency range ScaledmodelresultsareplottedinFigs.6and7.Predictions (5–65GHz)areperformedbiasingthedeviceat V, arecomparedbothtothescalablemodeldescribedin[20]and V mA , which corresponds to the typical the linear scalable foundry model. It must be pointed out that condition for the design of a power amplifier (PA) working in thefoundrydesignkitdoesnotprovideasinglescalablemodel, class-Aoperation. but different linear scalable models, each one extracted for a Following the identification procedure described in givennumberoffingers;thus,thefingerwidthistheonly“true” Section II-B, the measurements are deembedded from the scalingvariableavailable.Thefoundrymodelsarerelatedtothe parasitic elements in order to obtain the intrinsic measured operating bias condition V and mA/mm admittance parameters. These data can be used for the iden- (whichcorrespondstothescaledclass-Aoperatingconditionof tification of any intrinsic linear (or nonlinear) device model. our6 50 mreferencedevice). However,since the aim of this study is to investigate the scal- Accuracyimprovementswithrespecttothemodelpresented ability of the proposed extrinsic parasitic modeling approach, in[20]areevidentfromFigs.6and7.Thisisduetothemod- we prefer to avoid using any particular model for the intrinsic ified scaling rules and the improved extraction procedure pro- 250 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.57,NO.2,FEBRUARY2009 Fig.8. MAGversusnumberofgatefingersandfingerwidthsat30GHzevalu- atedthroughtheproposedmodel.TheblackdotsaretheMAGvaluesmeasured onactualdevicesamples.Boldlineshighlightthedifferencesbetweenmeasured andsimulatedvalues. easilyscalablewithrespecttotheunitgatewidthonlysincedata ofdifferentEMsimulationsarerequiredtomodelthechangein the number of fingers. For this reason, the number of fingers cannotbeusedassweptoroptimizationvariable. TheexperimentalresultsinFigs.6and7highlightthepredic- tionaccuracyoftheproposedscalablemodelforawidesetof deviceswithinthetechnologicalprocessundertest.Thisleads the quite interesting opportunity of evaluating the way typical designparametersvaryasafunctionoflayoutparameters,such asthenumber ofgatefingersandthegatewidth .Itisim- portantto notice thatthis task cannot always be accomplished bysimplysweepingsuitablescalingvariables.Forexample,the providedfoundrymodelnecessarilyinvolvesaseparatesimula- tionforeachdifferentnumberofgatefingers. TheMAGisshown,forinstance,inFig.8,with ranging from4to12,and from30to100 m.Theseresults,which have been obtained by simply, continuously sweeping the scalingvariables,areingoodagreementwithqualitativeexpec- tations [1], i.e., the simulated MAG is nearly constant versus Fig.7. (cid:0)-parametersversusfrequencyforthe6(cid:0)50(cid:2)m:(a)referencedevice the number of fingers at fixedgatewidth, while it decreases as andthelargest(cid:0)12(cid:0)75(cid:2)m(cid:2)(b)scaleddevice.Measurements(circles)versus thedevicegatewidthincreases. predictionsobtainedthroughdifferentscalablemodels:proposedmodel(bold lines),model[20](lines),andfoundrymodel(dots).Theresultsrefertothe Thesameexperimenthasbeenrepeatedbyusingthescalable devicebiasedintypicalclass-Aoperation. foundrymodelinvolvingaseparatesimulationforeachdifferent numberofgatefingers.Thecorrespondingresultsareshownin Fig.9. posedinthispaper.Inaddition,experimentalresultsinFigs.6 Predicted and actual measured values of the MAG for the and7pointoutthatthenewscalablemodelisatleastasaccu- available device sizes are reported in Table III. The results rateasthemostadvancedfoundrylinearscalablemodels.This quantitativelyshowthattheproposedmodelaccuratelypredicts isaninterestingresultconsideringthattheproposedmodelhas (even slightly better than foundry model) the gain variations beenobtainedbyexploitingtheminimumamountofEMsimu- with respect to the unit gatewidth. Deviations reported in lateddataandasinglesetof -parametermeasurementscarried TableIIIarealsographicallyhighlightedinFigs.8and9. outforasinglereferencedeviceattherequiredoperatingcon- Theresultspresentedinthissectionshowthatalumpedrep- dition.Onthecontrary,thefoundrymodelisextractedbyusing resentation of the extrinsic parasitic phenomena, identified by bothEMsimulations,aswellasadditionalmeasurementsper- meansofsuitableEMsimulations,leadtoaanaccuratescalable formedondifferent-in-sizedevices,evenconsideringbiascon- modelcoveringallthepossibledevicesizesactuallymanufac- ditions different with respect to the operating one. More pre- turedbythefoundry. cisely,EM-baseddatamatricesareusedforthemodelingofthe access structures, while the additional measurements are used IV. EXAMPLEOFOPTIMUMPERIPHERYSELECTION inordertoextracttheparasiticelementsatthefingerregionref- erence planes (mixed physical–empirical scaling rules are de- Apracticalexploitationexampleoftheadvantagesprovided rivedatthesereferenceplanes).Thefoundrymodelis,therefore, by the proposed scalable modeling approach is provided here. RESCAetal.:SCALABLEEQUIVALENTCIRCUITFETMODELFORMMICDESIGNIDENTIFIEDTHROUGHFW-EMANALYSES 251 Fig.9. MAGversusnumberofgatefingersandfingerwidthsat30GHzeval- Fig.10. Stabilityfactor(cid:0)versusnumberofgatefingersandfingerwidthsat uatedthroughthefoundrymodel.TheblackdotsaretheMAGvaluesmeasured 30GHzevaluatedthroughtheproposedmodel.Thegrayplanecorrespondsto onactualdevicesamples.Boldlineshighlightthedifferencesbetweenmeasured the(cid:0) (cid:0) (cid:2)threshold. andsimulatedvalues. TABLEIII MEASUREDVERSUSMODELEDMAG@30GHz Let us consider the goal of selecting the optimum device pe- riphery for the design of a narrowband linear driver amplifier workingat30GHz. Differentcriteriacanbeadoptedforthechoiceoftheelemen- Fig.11. Loadandsourcereflectioncoefficients((cid:3) and(cid:3) )providinginput/ tarydevicecelltobeparalleledinordertoachievetherequired outputsimultaneousconjugatematchversusnumberofgatefingersandfinger widths((cid:0)and(cid:2))at30GHz.(cid:0)varyingfrom4to12numberoffingers(even outputpower.Afirstselectioncouldbebasedonthemaximiza- numbers),(cid:2) varyingfrom30to100(cid:3)m,step5(cid:3)m.Thearrowsshowhowthe tionofMAG,whensimultaneousinput/outputconjugatematch reflectioncoefficientsvarywhentheindependentvariablesincrease. (SCM) conditions are satisfied [2]. On the other hand, termi- nating impedances providing SCM can be only considered if thetransistorisunconditionallystableatthedesiredfrequency. V. CONCLUSION Inordertotestthiscondition,thestabilityfactor isevaluated Anewscalablemodelingapproachhasbeenpresentedinthis versusthedeviceperipherybyconsidering paper.Itisbasedonthedefinitionofalumpedcomponentde- and m.Tothisaim,trivial -param- scriptionoftheextrinsicparasiticnetwork,whichisprovento etersimulationsareautomaticallyrepeatedbysweepingthe be perfectly scalable with the number of gate fingers and the and variables.CorrespondingresultsarepresentedinFig.10, corresponding finger width. The device scalable parasitic ele- showing that most of the investigated peripheries are in this ments are identified by using only EM simulation data of just caseunconditionallystableat30GHz.Analogously,sourceand onereferencedevice.Thismeansthatneitherdevicemeasure- loadreflectioncoefficients( and ),providinginput/output mentsinconvenientconditionsofpassivity(i.e.,pinched-offor SCMconditions,areplottedontheSmithChartversus and forward-gatecoldFETconditions),nordifferent-in-sizedevice in Fig. 11. Optimum periphery selection can be easily car- measurementsarerequiredfortheextrinsicelementextraction. riedoutonthebasisoftheseresults,according tosuitable de- Theextrinsicequivalentcircuitelementsarecorrectlylinked signconstraintssuchasgain,sensitivitytoparametervariations, to the device layout, allowing the model to scale with simple physicalfeasibilityofthematchingnetworks,stabilitymargin, linear rules related to geometric-based scaling factors. Such and so on. scaling rules are process independent since they are neither The results shown in Figs. 8, 10, and 11 are easily and im- completely empirical, nor fitting based. Besides its simple mediately obtained by means of the proposed model. Instead, definition and identification procedure, the proposed scalable the same investigation would require separate sets of simula- model provide good accuracy in the prediction of different tions(oneforeachdifferentnumberofgatefingers),whenusing deviceshavingdifferentperipheries. the foundry model. This limitation could become dramatic if Finally,theproposedmodelallowsthedesignertousethede- more complex optimization problems involving and as vicegeometricalparameters(inthiscase,thenumberoffingers unknownparameterswereconsidered. andunitgatewidth)assweptandoptimizationvariables.

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