硅超大规模集成电路工艺技术—理论、实践与模型-课后习题答案

1.2.Assumingdopantatomsareuniformlydistributedinasiliconcrystal,howfarapartaretheseatomswhenthedopingconcentrationisa).1015cm-3,b).1018cm-3,c).5x1020cm-3.Answer:Theaveragedistancebetweenthedopantatomswouldjustbeoneoverthecuberootofthedopantconcentration:xNA1/3a)x1x1015cm31/31x105cm0.1m100nmb)x1x1018cm31/31x106cm0.01m10nmc)x5x1020cm31/31.3x107cm0.0013m1.3nm1.3.Considerapieceofpuresilicon100µmlongwithacross-sectionalareaof1µm2.Howmuchcurrentwouldflowthroughthis“resistor”atroomtemperatureinresponsetoanappliedvoltageof1volt?Answer:Ifthesiliconispure,thenthecarrierconcentrationwillbesimplyni.Atroomtemperature,ni≈1.45x1010cm-3.Underanappliedfield,thecurrentwillbeduetodriftandhence,IInIpqAninp1.6x1019coul108cm21.45x1010carrierscm32000cm2volt1sec11volt102cm4.64x1012ampsor4.64pA1.10.Astate-of-the-artNMOStransistormighthaveadrainjunctionareaof0.5x0.5µm.Calculatethejunctioncapacitanceassociatedwiththisjunctionatanappliedreversebiasof2volts.Assumethedrainregionisveryheavilydopedandthesubstratedopingis1x1016cm-3.Answer:ThecapacitanceofthejunctionisgivenbyEqn.1.25.CASxdqS2NANDNAND1iVThejunctionbuilt-involtageisgivenbyEqn.1.24.NDisnotspecifiedexceptthatitisverylarge,sowetakeittobe1020cm-3(roughlysolidsolubility).TheexactchoiceforNDdoesn'tmakemuchdifferenceintheanswer.ikTqlnNDNAni2.0259voltsln1020cm31016cm31.45x1010cm320.934voltsSinceNDNAinthisstructure,thecapacitanceexpressionsimplifiestoCASWqS2NA1iV1.6x1019coul11.71016cm38.86x1014Fcm122.934volts1.68x108Fcm2Giventheareaofthejunction(0.25x10-8cm2,thejunctioncapacitanceisthus4.2x10-17Farads.3.2.Aboron-dopedcrystalpulledbytheCzochralskitechniqueisrequiredtohavearesistivityof10Ωcmwhenhalfthecrystalisgrown.Assumingthata100gmpuresiliconchargeisused,howmuch0.01Ωcmborondopedsiliconmustbeaddedtothemelt?Forthiscrystal,plotresistivityasafunctionofthefractionofthemeltsolidified.Assumek0=0.8andtheholemobilityµp=550cm2volt-1sec-1.Answer:Usingthemobilityvaluegiven,and1qNAwehave:10ΩcmNA=1.14x1015cm-3and0.01ΩcmNA=1.14x1018cm-3FromEqn.3.38,CSCOkO1fkO1andwewantCS=1.14x1015cm-3whenf=0.5.Thus,solvingforC0theinitialdopingconcentrationinthemelt,wehave:C01.14x10150.810.50.21.24x1015cm3ButC0I0V0#ofimpuritiesunitvolofmelt(Doping)(Vol.of0.01cm)Vol100gmSiWgtaddedof0.01cmSi=C0Doping100gm0.109gmTheresistivityasafunctionofdistanceisplottedbelowandisgivenbyx1qNAx1f1k0qC0k011.5cm1f0.20Resistivity0.20.40.60.81FractionSolidified-f3.3.ACzochralskicrystalispulledfromameltcontaining1015cm-3boronand2x1014cm-3phosphorus.InitiallythecrystalwillbePtypebutasitispulled,moreandmorephosphoruswillbuildupintheliquidbecauseofsegregation.AtsomepointthecrystalwillbecomeNtype.AssumingkO=0.32forphosphorusand0.8forboron,calculatethedistancealongthepulledcrystalatwhichthetransitionfromPtoNtypetakesplace.Answer:WecancalculatethepointatwhichthecrystalbecomesNtypefromEqn.3.38asfollows:CSPhosC0k01fk012x10140.321f0.68CSBoronC0k01fk0110150.81f0.2Atthepointwherethecross-overoccurstoNtype,thesetwoconcentrationswillbeequal.Solvingforf,wefindf0.995Thusonlythelast0.5%ofthecrystalisNtype.3.6.SupposeyourcompanywasinthebusinessofproducingsiliconwafersforthesemiconductorindustrybytheCZgrowthprocess.Supposeyouhadtoproducethemaximumnumberofwafersperboulethatmetafairlytightresistivityspecification.a).WouldyouprefertogrowNtypeorPtypecrystals?Why?b).WhatdopantwouldyouuseingrowingN-typecrystals?WhatdopantwouldyouuseingrowingPtypecrystals?ExplainAnswer:a).Boronhasthesegregationcoefficientclosesttounityofallthedopants.ThusitproducesthemostuniformdopingalongthelengthofaCZcrystal.ThusPtypewouldbethenaturalchoice.b).ForPtype,theobvious(andonlyrealchoice)isboronasexplainedinparta).ForNtypecrystalsFig.3-18showsthateitherPorAswouldbeareasonablechoicesincetheirsegregationcoefficientsarequitecloseandarebetterthanSb.Table3-2indicatesthatPmightbeslightlypreferredoverAsbecauseitskOvalueisslightlycloserto1.4.1.AnICmanufacturingplantproduces1000wafersperweek.Assumethateachwafercontains100die,eachofwhichcanbesoldfor$50ifitworks.Theyieldonthesechipsiscurrentlyrunningat50%.Iftheyieldcanbeincreased,theincrementalincomeisalmostpureprofitbecauseall100chipsoneachwaferaremanufacturedwhethertheyworkornot.Howmuchwouldtheyieldhavetobeincreasedtoproduceanannualprofitincreaseof$10,000,000?Answer:At1000wafersperweek,theplantproduces52,000wafersperyear.Ifeachwaferhas50gooddieeachofwhichsellsfor$50,theplantgrossincomeissimplyIncome=(52,000)(50)($50)=$130,000,000peryear.Toincreasethisincomeby$10,000,000requiresthattheyieldincreaseby101307.7%4.3.AsMOSdevicesarescaledtosmallerdimensions,gateoxidesmustbereducedinthickness.a.Asthegateoxidethicknessdecreases,doMOSdevicesbecomemoreorlesssensitivetosodiumcontamination?Explain.b.Asthegateoxidethicknessdecreases,whatmustbedonetothesubstratedoping(o