Calculation of the Current Response of the Spatially Modulated Light CMOS Detector

CalculationoftheCurrentResponseoftheSpatially

ModulatedLightCMOSDetector

areaof1mmJanGenoe,DanniëlCoppée,Member,IEEE,JohanH.Stiens,RogerA.Vounckx,Member,IEEE,andM.Kuijk,Member,IEEE

Abstract—Wepresentananalyticalmodelthatallowstocalcu-latethecurrentresponseofaspatiallymodulatedlightCMOSde-tector(SML-detector)andcomparethisresponsewiththeresponseofatraditionalCMOSphotodetector.ItisshownthattheSMLde-tectoralreadyyieldsathreeordersofmagnitudefasterresponsetimethanatraditionalCMOSdetectorina0.25mCMOStech-Wnology.ThisresponsetimewillfurtherdecreaseasCMOStech-[5]channelat200Mb/swithabiterrorratebelownologyevolves.Thisanalyticalexpressioniscomparedwithanu-mericalsolutionofthediffusionequationandwithexperimentaldevelopmentofananalyticalmodelforthecalculationoresults.Bothshowanexcellentcorrespondence.ThereforewecanintrinsicSML-detectorresponseistheobjectofthispapeconcludethattheSML-detectoristhesolutionofchoiceforcheap,CMOS-compatiblereceiversinintegratedopto-electronicsystems.

IV/13,andAWI:GOA20325.ThereviewofthispaperwasarrangedbyP.Bhattacharya.J.GenoeiswiththeETRO-IMECDepartment,VrijeUniversiteitBrI.INTRODUCTION

BrusselsB-1050,BelgiumandalsowiththeKHLim,DiepenbeekB-359LECTRICALinterconnectionsbetweengiumintegratedcir-D.Coppée,J.H.Stiens,R.A.Vounckx,andM.Kuijkarewcuitssuffernowadaysfromlackofaggregatebandwidth,ETRO-IMECDepartment,VrijeUniversiteitBrussels,BrusselsBelectromagneticinterference(EMI),electromagneticcompati-Belgium.PublisherItemIdentifierS0018-9383(01)06912-X.bility(EMC),ESDproblemsandtoohighpowerconsumption.

receivedAugust21,2000;revisedMarch28,2001.ThiswoIndexTerms—CMOSanalogintegratedcircuits,Manuscriptopticalre-supportedinpartbyEC:ESPRITIV-MELARI-OIIC,FWOV,DWTC:ceivers,photodetectors.

E

Connectingintegratedcircuitswithopticalchannelsmay

possiblyalleviatemostoftheseproblems.Opticalsolutionsareinvestigatedanddevelopedforparallelopticalinterconnectsbetweenchipsandforseveralothercommunicationsystems,suchasGigabitEthernet,

0018–938GENOEetal.:SPATIALLYMODULATEDLIGHTCMOSDETECTORFig.1.SML-Detectorcrosssection(top)andmasklayout(bottom).Thedotssymbolizethephotogeneratedcarriersatilluminationmomentt=t

t

ttthttththttttttttotttthttthttttththttttattthtthttothttttttttttttthtthtttttottthttttthtrthtttt13

tttttttthttthtththttothttththtothtottthttthtttttttttothtththt14IEEETRANSACTIONSONELECTRONDEVICES,VOL.48,NO.9,SEPTEMBER2001

Duetothefactthattheelectricfield

isabout

in

/V/s,cm

s,and

increasesto

m,wewillcomparetheanalyticalandnumerical

results.Areversebiasvoltageof3.3Vwasappliedoverthedetectorandtheequilibriumminoritycarrierprofile(comparedtobulkmaterial)wasusedasthestartingpointofthesimula-tion(i.e.,theprofileatthemoment).Thisimpliedthatbe-forethesimulationstartedallminoritycarrierdensitieswerenegativenumbers.Theimmediateregionwasfirstilluminatedduring5psafter

ps.Someobtainedminority-carrierprofiles

areshowninFig.3.Itshouldbenotedthattheverticalscaleofthesefiguresis10timessmallerthanthehorizontalscale.Thefirstprofileshowstheminoritycarrierdensityattheendoftheillumination(

ps.Sothephotogeneratedcurrent

atbothcontactswillpersist,evenlongaftertheincidentlightpulse.

Wecanobtaintheimmediate

andthedeferred–

theelectrongenerationrateatthelowerborderofthe

spacechargeregion.Itcanbeexpressedasafunctionofthe

incidentlightflux

as(5)

withthedistancebetweenthesurfaceandthelowerofthe

spacechargeregion.WetooktheLaplacetransformofthetimevariable

(6)

ABodeplotofthisresponseisshownasthedashedlineinFig.5.Equation(6)showsthat,fromthe3dBfrequency

isapplied,the

photogeneratedcarrierprofile

,i.e.,theconditionapplies(seeFig.1).Inordertoobtainarealisticestimateoftheimmediateanddeferred

GENOEetal.:SPATIALLYMODULATEDLIGHTCMOSDETECTOR15

Fig.3.Calculatedexcesscarrierprofilebelowthepnjunctionaftera5pslightpulseincidentona2󰀖mperiodSMLdetector.Thisprofileisrecordedforseveralmomentsoftime(5ps,10ps,22ps,54ps,70ps,and400ps).

current,thediffusionequation(3)needstobesolvedintwodimensions.Duetotheperiodicnatureofthestructureof(3)inthe

asaFourierse-

16IEEETRANSACTIONSONELECTRONDEVICES,VOL.48,NO.9,SEPTEMBER2001

Fig.4.Theimmediate(I)anddeferred(D)currentdensitiesextractedfromthenumericalsimulationsgiveninFig.3asafunctionoftime.ThedifferencebetweenbothcurrentsisgivenasI-D.TheinsetshowsthetheoreticalcalculationusingtheinverseLaplacetransformsof(6)and(9)forthesamestructure.

rieswiththeperiodicityofthefingerpattern.Equation(3)canonlybefulfilledforeveryvalueof

andnot90

.Firstthecarrierprofileiscalculatedbytakingthe

Laplacetransformofthetimevariable

(otherwise,thereisnoadvantagein

usinganSMLdetector):

and

of20

mresultsinamaximalfrequencyofabout422MHz,

andagridperiodicityof5

-.Thehigherordersolutionsarealluneven

innatureanddonotcontributeto

.Thesumofallthesecontributionsyields

(9)

Equation(9)hasbeenusedtocalculatethefrequencyandphaseresponseoftheelectroncurrentofthreetypicalSMLdetectors,

mand4i.e.,adetectorwithagridperiodicityof20

GENOEetal.:SPATIALLYMODULATEDLIGHTCMOSDETECTOR17

Fig.5.BodediagramoftheSML-detectorelectroncurrentresponsecomparedtotheconventionalCMOSdetector(dashedline).Severaldetectorfingerperiods(L)aregiven.Whenbothamplitudeandphaseareflat,nodistortionisobservedinthedetectorsignal.

ofnotperpendicularincidentlight.Butthisstudygoesbeyondthescopeofthispaper.

IV.CARRIERPROFILEABOVETHEJUNCTIONS

SPACECHARGEREGION

Inthissection,wecalculatetheminoritycarrierprofileabovethejunction,whichisinthiscaseaholeprofile.Holesareassuchslowerthanelectronsandatfirstglance,onewouldex-pectaslowerresponsecurrentformthephotogeneratedholes.However,currentstateoftheartintegratedcircuittechnologyimplementsextremelyshallown

Inthefirstapproach,wecanconsideranalmostconstantholegenerationintheareaabovethePNjunction.Theequilibriumexcessholeconcentrationiszeroatallbordersurfaces:Atthetopsurfaceduetosurfacerecombinationandattheothersur-facesduetothepresenceoftheelectricalfield.However,thephotogeneratedholeconcentrationisonlyzeroatthethreejunc-tionbordersandnotatthesurface,becausethesurfacerecom-binationprocessisfarslowerthanthefrequenciesconsideredinthispaper.Theminoritycarriercurrentthroughthetopsurfaceishoweverzero,becausethereisnotopcontactaboveanillu-minatedpartofthewell.

Inordertocalculatetheholeresponsecurrent,wesolvedthetransportequationfortheholesbeing

current.

18IEEETRANSACTIONSONELECTRONDEVICES,VOL.48,NO.9,SEPTEMBER2001

Withbeing

andholeshavebeendiscussedintheprevioussections.Thecurrentdensityresponseofthespacechargeregion(SCR)willalwaysbemuchfasterthanthereadoutamplifierresponseandcanbeconsideredjustproportionaltothelightabsorptionuptofrequenciesequaltotheinverseoftheSCR-transittime.Becausethesefrequenciesarefarbeyondthemaximumfre-quenciesweconsider,theresponseofthespacechargeregionequals

-typelayer(1.5mm)andisthehole

livetimeintheN-typelayer(2.5ms)[6].Thecarrierdistribu-andthecarriergenerationfunctionaretionfunctionp

rewrittenastheproductoftwoFourierseries,oneofasquarewaveinthex-direction(havingindexn)andtheotherofasquarewaveinthey-direction(havingindex

drivesoneofthetermsofdecomposedof

p

.Itcanbeseenfrom(12)thattheamplitudeof

theothercontributionsdecreasesquadraticwithnandm.There-fore,iftheholediffusionisthefrequencylimitofthedetector,themaximumdetectorfrequencyisdeterminedby

doesdependonthedopinglevel.Forthestructures

cmunderconsideration,itcanbeestimatedas

is

substantiallyhigherthan

-m,awellspacingbeingm.Theseparateelectronand3

holecontributionstothecurrentandthecurrentofthespacechargeregionarealsoshown.Thedominantcurrentistheelec-troncurrent,whichhasits3dBfrequencyaround450MHz.Theholeresponsehasits3dBfrequencyaround5GHz.Fi-nally,alsoaflatresponseisobtained,correspondingtocarriersgeneratedinthespacechargeregion.Inthediscussiononintersymbolinterference(nextsection)wewillpointoutwhichmax-imumsignalfrequencythatcanbeobtainedstartingfromtheseresponsefunctions.

Withasamplingperiod

isthecurrentresponsefunctioninthetimedomain.ItcanbeobtainedfromtheinverseLaplacetransformationsof(9),(12)and(15).Theintersymbolinterferencecanbeexpressed

GENOEetal.:SPATIALLYMODULATEDLIGHTCMOSDETECTOR19

Fig.6.BodediagramofthecombinedI–DSMLdetectorresponseforadetectorwithawellwidthbeing2󰀖m,awellspacingbeing3󰀖mandawelldepthbeing1.5󰀖m.Theresponseoftheelectroncurrentandholecurrentisalsogiven(dotted).

asafixedoffset

severalsignaltonoiselevels.ItisobservedthataconventionalCMOSdetector(ms)cannotobtainaBERbelow10

anderrorcorrectionsschemesallowtheapplicationinthe100Mb/srange,buttheGb/srangeformsafundamentallimit.The10

.This3Gb/sis

substantiallyabovethein(10)calculated

oftheSMLdetectoris

indicativeforthemaximumbitrate,butthemaximumfrequencydependsontherandomnessofthebitstream,theS/Nratio,andthemaximumallowableBER.Themaximumbitrateisinanycasesubstantiallybeyondthefrequency

(17)

With

theprobabilityofhavingadigitalone

equals

–

mgridperiodicityfabricatedina0.6

mperiodicity,andthisfor

,and

waveformsontheabovedescribedSMLCMOSdetectorafteranincidentbasebandbinarydatastreamof300Mb/s.Itis

signalistheonlysignalobtainedwithoutobviousthatthe

shapedeformation.

1900IEEETRANSACTIONSONELECTRONDEVICES,VOL.48,NO.9,SEPTEMBER2001

Fig.7.BiterrorrateversusdatarateforaconventionalCMOSdetectorandan10󰀖mperiodicitySMLdetector,forseveralsignaltonoiseratios(S/N).

Fig.8.Measuredresponsivityasafunctionoffrequencyfora15.6-󰀖mgridperiodicitySMLdetector.AflatI-Dcurveisobtainedupto500Mb/s.

VIII.EVOLUTIONOFTHEFREQUENCYRESPONSE

VERSUSTECHNOLOGY

Fig.10plotsthemaximalSMLCMOSdetectorfrequency(n-wellimplementation)asafunctionoftheminimalgatelengthofthetechnology.ThecentrallineinbothgraphsofFig.10indicatesalatticeperiodicityobtainedfromthe

.Othersystems

thattrytorecovertheoriginalbinarydatafromthedistorteddatacannotusesimplethresholdlogicandrequireedgedetectioncircuitryorvariablethresholdlogic.Thismakesthemdefinitelymuchmoresensibletonoise,andthesesystemsneedasaconse-quenceanelaboratedencodinganderrorcorrectionsystem.AnSMLdetectorsystemcanbeoperatedwithoutorwithasimpleerrordetectionandcorrectionschemeuptheveryhighfrequen-cies.Thesefrequencieswillfurtherrisewithtechnology.TheoutlookdescribedaboveindicatesthattheSML-CMOShasin-deedallmajorcapabilitiestobecomethesolutionofchoicefor

GENOEetal.:SPATIALLYMODULATEDLIGHTCMOSDETECTOR1901

Fig.10.Maximaln-wellSMLCMOSdetectorfrequencyfasafunctionofthegatelengthoftheusedtechnologyforlightat825nm.TheyearsusedintheannotationsindicateinwhichyearthistechnologycanbeusedfortheproductionofASICs[12].Thegrayareaindicatesthediffractionlimitfortheusedlight.

cheap,CMOScompatiblereceiversinintegratedoptoelectronicsystems.

REFERENCES

[1]R.Vounckx,P.Heremans,D.Coppée,R.Windisch,G.Borghs,andM.

Kuijk,“Opticalchipinterconnects:Economicallyviable,”Proc.SPIE,vol.3491,p.294,1998.

[2]M.Ghioni,F.Zappa,V.P.Kesan,andJ.Warnock,“AVLSI-compat-iblehigh-speedsiliconphotodetectorforopticaldatalinkapplications,”IEEETrans.ElectronDevices,vol.43,p.1054,July1996.

[3]M.Kuijk,D.Coppée,andR.Vounckx,“Spatiallymodulatedlightde-tectorinCMOSwithsense-amplifierreceiveroperatingat180Mb/sforopticaldatalinkapplicationsandparallelopticalinterconnectsbe-tweenchips,”IEEEJ.Select.TopicsQuantumElectron.,vol.4,p.1040,Nov./Dec.1998.

[4]D.Coppée,W.Pan,J.Stiens,R.Vounckx,andM.Kuijk,“Experimental

studyofthespatially-modulatedlightdetector,”SolidStateElectron.,vol.43,p.609,1999.

[5]M.Kuijk,D.Coppée,J.Genoe,andR.Vounckx,“Paralleldetector/re-ceiverinstandard0.6󰀖mCMOSof100channelson1mm

1902IEEETRANSACTIONSONELECTRONDEVICES,VOL.48,NO.9,SEPTEMBER2001

MaartenKuijk(M’93)wasborninCanadain1965.HereceivedthePh.D.degreeinelectricalengineering(withhonors)fromtheVrijeUniversiteitBrussels(VUB),Belgiumin1993.Theworkwasfocusedontheoptoelectronicopticalthyristordeviceandonthedifferentialpairofopticalthyristorsresultingtherebyinfastandsensitiveopticaldigitaltransceivers.

In1994,hebecameAssistantProfessorattheVUBinthefieldofintegratedelectronicsandopto-electronicsandwasadditionallyappointed

“ResearchAssociate”forthefundforscientificresearchFlanders(FWO-V)in1997.Hiscurrentresearchtopicsincludeelectricalandopticalinterconnects,devices,opticalcomponents,CMOScircuits,andalternativesforflip-chiptechnology.Heauthoredandco-authoredmorethan40internationalrefereedpublications,holdingthreeinternationalpatents,eightpatentspending.Oneoftheapprovedpatentsconcernsthe“SpatiallyModulatedLight”detector.ThenoveldetectorprincipleallowsintegrationoffastdetectorsinstandardCMOSoperatingatcommunicationbitratesashighas1Gb/s.