A Scalable Substrate Noise Coupling Model for Mixed-Signal I

Abstract—A scalable macromodel for substrate noise coupling in heavily doped substrates has been developed. This model is simple since it requires only four parameters which can readily be extracted from a small number of device simulations or measurement

AScalableSubstrateNoiseCouplingModel

forMixed-SignalICs

KartiMayaramTerriFiezSchoolofEECSDepartmentofECE

SiliconLaboratoriesInc.WashingtonStateUniversityOregonStateUniversityAustin,TX78735,USAPullman,WA99164,USACorvallis,OR97331,USA

AnilSamavedam

Abstract—Ascalablemacromodelforsubstratenoisecouplinginheavilydopedsubstrateshasbeendeveloped.Thismodelissimplesinceitrequiresonlyfourparameterswhichcanreadilybeextractedfromasmallnumberofdevicesimulationsormeasurements.Oncetheseparametershavebeendeterminedthemodelcanbeusedforanyspacingbetweentheinjectionandsensingcontactsandfordifferentcontactgeometries.Thescalabilityofthemodelwithseparationandwidthprovidesinsightintosubstratecouplingandoptimizationissuespriortoandduringthelayoutphase.Themodelisvalidatedfora2manda0.5mCMOSprocesswhereitisshownthatthesimplemodelpredictsthenoisecouplingaccurately.Measurementsfromachipfabricatedina0.5mCMOSprocessshowgoodagreementwiththemodel.

I.INTRODUCTION

Substratecouplinginmixed-signalCMOSICscandegradetheperformanceifitisnotwellcharacterized.Todate,modelsforsubstratecouplingareusedaspartofthe nallayoutextractionandsimulationveri cation.Severaltechniqueshavebeenpro-posedforanalyzingsubstratecouplinginintegratedcircuits[1-10].Thesubstratemodelsdevelopedarebasedon nitediffer-encemethods[7,10],boundaryelementmethods[3],andpoly-nomialcurve ttingmethods[2,6].Reduced-ordermacromodelscanalsobeobtainedusingtechniquesbasedonAWEorArnoldimethods[7,9].Thesemodelsaredif culttouseintuitivelyaspartofthedesignprocess.

Inthispaper,asubstratecouplingmacromodelisdescribedthatcanbeusedduringtheearlystagesofdesignandsimulation.Foragivenprocess,simplecurve ttingisusedtodetermineafewparametersusedinthemodel.Thismodelscaleswiththesubstratecontactseparationdistanceandtheareaoftheinjectorandsensorcontacts.Itcanalsobeusedtodeterminethesub-stratecouplingbetweentransistors.Thepaperbeginswithade-scriptionofthegeneralmodelinSectionIIforap-typesubstrate.InSectionIII,thescalingofthemodelwiththecontactsizeisdescribed.SectionIVextendsthemodeltocouplingbetweenn+-p+contacts.ExperimentalresultsarepresentedinSectionVandconclusionsarepresentedinSectionVI.

II.SUBSTRATECOUPLINGMACROMODELS

Substratecouplingmodelsarenecessarytoaccuratelypredictthecouplingbetweencircuitssharingthesamesubstrate.Asub-ThisworkissupportedinpartbytheNSFCenterfortheDesignofAnalog/DigitalIntegratedCircuits(CDADIC)andunderNSFcontractCCR-9702292.

0-7803-5832-X /99/$10.00 ©1999 IEEE.

stratemacromodelwhichscalesdirectlywiththeseparation,sizeandshapeofthecontactsonadiecanbeusedtogenerateanetlist leforacircuitsimulatorgiventhelayoutandprocessinforma-tionasshowninFig.1.Suchamodelcanofferinsightintothedependenceofcouplingonsizes,shapesandplacementofdiffer-entstructuresonthedieandcancutdownontheoveralldesigntime.Further,suchmodelscanbeusedtooptimizetheplacementofstructuresforimprovedisolation.

Fig.1.Generationofascalablesubstratemacromodelfromlayouttobeusedinacircuitsimulator.

ForfrequenciesofafewGHzandbelow,thesubstratecanbetreatedasaresistivenetwork[7].InFig.2(a),thecrosssectionofatypicalheavilydopedsubstrateisshown.ThisstructurecanbesimulatedusingthedevicesimulatorTMA-Medici[11]tode-terminethecouplingbetweenpointsAandB.Thecouplingischaracterizedintermsof-parameterswherebyanACvoltageisappliedatoneportandthecurrentsaremeasuredwiththeotherportconnectedtoground.

SimulationswithMedicivalidatethatbelow2GHz,theheavily-dopedsubstratecanbemodeledasalumpedresistivenetwork.Simulationsalsoshowthatforcontactspacingsoflessthan10m,nearlyallthecurrent owsonthesurfacebetweenthetwocontacts.However,foracontactspacinggreaterthan100m,nearlyallthecurrent owsdownintothe(verylowre-sistive)substrate.ThisisillustratedinFig.2(b)wherethecurrentisshownto owdownintothesubstrate.

Themacromodelforthesubstratefortwopointcontactson

thesubstrateisshowninFig.3(a).Here

,andaretheconductances.Thebackplanecontactofthesubstrateiscon-nectedtoground.Ifthecontactsareofthesamesizeandshape

then

.ThetwoportY-parametersforthesubstratemacromodelarethengivenby,

(1)

Abstract—A scalable macromodel for substrate noise coupling in heavily doped substrates has been developed. This model is simple since it requires only four parameters which can readily be extracted from a small number of device simulations or measurement

Sensor

5u

(a)(b)

Fig.2.(a)CrosssectionofaheavilydopedCMOSsubstratewithpointcontactsand(b)current owlinesfromdevicesimulationsfor100mseparationbetweentheinjectionandsensorcontacts.

(a)(b)

Fig.3.(a)Macromodelforthesubstratewhenthebackplaneisgrounded.(b)ModelfornoisecouplingbetweenaN-sourceandP-sensor.

TheZ-parameterscanbecomputedbyinvertingtheY-matrixandaregivenby:

(2)

whereisthedeterminantofthetwo-portY-matrixandisgiven

by:

(3)

Solvingfor

(4)

whereisaconstant[6].Rearrangingthisexpression:

(5)

Ifeither

orisgivenasafunctionofdistance,theothercanbeobtainedbysolvingtheaboveequation.Fromdevicesim-ulations,increasingthespacingbetweencontactsincreases(de-creases)thevalueof

().Theactualvaluesofandcanbedeterminedfrom2-Ddevicesimulationsormeasurements.

Thevalueof

determinedfromMedicisimulationsasafunc-tionofcontactspacingisshowninFig.4(a)fora0.5manda2mCMOSprocess,respectively.Thelineardependenceonthe

semilogplotof

canbemodeledbyanexponentialdependenceon:

(6)

whereandareconstantsdeterminedfromsimulatedormea-sureddata.Onlytwopointsareneededtoobtainrelativelyaccu-rateresults.Theaccuracyofandcanbeimprovedwithmore

(a)

(b)

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