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.docx

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.docx

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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:

a）

b）

c）

1.3.Considerapieceofpuresilicon100µmlongwithacross-sectionalareaof1µm2.Howmuchcurrentwouldflowthroughthis“resistor”atroomtemperatureinresponsetoanappliedvoltageof1volt?

Answer:

Ifthesiliconispure,thenthecarrierconcentrationwillbesimplyni.Atroomtemperature,ni≈1.45x1010cm-3.Underanappliedfield,thecurrentwillbeduetodriftandhence,

1.10.Astate-of-the-artNMOStransistormighthaveadrainjunctionareaof0.5x0.5µm.Calculatethejunctioncapacitanceassociatedwiththisjunctionatanappliedreversebiasof2volts.Assumethedrainregionisveryheavilydopedandthesubstratedopingis1x1016cm-3.

Answer:

ThecapacitanceofthejunctionisgivenbyEqn.1.25.

Thejunctionbuilt-involtageisgivenbyEqn.1.24.NDisnotspecifiedexceptthatitisverylarge,sowetakeittobe1020cm-3（roughlysolidsolubility）.TheexactchoiceforNDdoesn'tmakemuchdifferenceintheanswer.

SinceND>>NAinthisstructure,thecapacitanceexpressionsimplifiesto

Giventheareaofthejunction（0.25x10-8cm2,thejunctioncapacitanceisthus4.2x10-17Farads.

3.2.Aboron-dopedcrystalpulledbytheCzochralskitechniqueisrequiredtohavearesistivityof10Ωcmwhenhalfthecrystalisgrown.Assumingthata100gmpuresiliconchargeisused,howmuch0.01Ωcmborondopedsiliconmustbeaddedtothemelt?

Forthiscrystal,plotresistivityasafunctionofthefractionofthemeltsolidified.Assumek0=0.8andtheholemobilityµp=550cm2volt-1sec-1.

Answer:

Usingthemobilityvaluegiven,and

wehave:

10Ωcm⇒NA=1.14x1015cm-3and0.01Ωcm⇒NA=1.14x1018cm-3

FromEqn.3.38,

andwewantCS=1.14x1015cm-3whenf=0.5.Thus,solvingforC0theinitialdopingconcentrationinthemelt,wehave:

Theresistivityasafunctionofdistanceisplottedbelowandisgivenby

3.3.ACzochralskicrystalispulledfromameltcontaining1015cm-3boronand2x1014cm-3phosphorus.InitiallythecrystalwillbePtypebutasitispulled,moreandmorephosphoruswillbuildupintheliquidbecauseofsegregation.AtsomepointthecrystalwillbecomeNtype.AssumingkO=0.32forphosphorusand0.8forboron,calculatethedistancealongthepulledcrystalatwhichthetransitionfromPtoNtypetakesplace.

Answer:

WecancalculatethepointatwhichthecrystalbecomesNtypefromEqn.3.38asfollows:

Atthepointwherethecross-overoccurstoNtype,thesetwoconcentrationswillbeequal.Solvingforf,wefind

Thusonlythelast0.5%ofthecrystalisNtype.

3.6.SupposeyourcompanywasinthebusinessofproducingsiliconwafersforthesemiconductorindustrybytheCZgrowthprocess.Supposeyouhadtoproducethemaximumnumberofwafersperboulethatmetafairlytightresistivityspecification.

a）.WouldyouprefertogrowNtypeorPtypecrystals?

Why?

b）.WhatdopantwouldyouuseingrowingN-typecrystals?

WhatdopantwouldyouuseingrowingPtypecrystals?

Explain

Answer:

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,theplantgrossincomeissimply

Income=（52,000）（50）（$50）=$130,000,000peryear.

Toincreasethisincomeby$10,000,000requiresthattheyieldincreaseby

4.3.AsMOSdevicesarescaledtosmallerdimensions,gateoxidesmustbereducedinthickness.

a.Asthegateoxidethicknessdecreases,doMOSdevicesbecomemoreorlesssensitivetosodiumcontamination?

Explain.

b.Asthegateoxidethicknessdecreases,whatmustbedonetothesubstratedoping（oralternativelythechannelVTHimplant,tomaintainthesameVTH?

Explain.

Answer:

a）.Fromthetext,Na+contaminationcausesthresholdvoltageinstabilitiesinMOSdevices.AlsofromEqn.4.1,thethresholdvoltageisgivenby

Asthegateoxidethicknessdecreases,COXincreases,sothesameamountofmobilechargeQMwillhavelesseffectonVTHasoxidesgetthinner.ThereforeMOSdevicesarelesssensitivetosodiumcontamination.

b）.UsingthesameexpressionforVTHasinparta）,weobservethatastheoxidethicknessdecreases,（COXincreases）,tomaintainthesameVTH,NAwillhavetoincrease.NAwillactuallyhavetoincreasebythesquarerootoftheoxidethicknessdecreasetokeepVTHconstant.

4.4.AnewcleaningprocedurehasbeenproposedwhichisbasedonH2OsaturatedwithO2asanoxidant.ThishasbeensuggestedasareplacementfortheH2O2oxidizingsolutionusedintheRCAclean.SupposeaSiwafer,contaminatedwithtraceamountsofAu,FeandCuiscleanedinthenewH2O/O2solution.Willthiscleanthewafereffectively?

Whyorwhynot?

Explain.

Answer:

Asdescribedinthetext,cleaningmetalionsoffofsiliconwafersinvolvesthefollowingchemistry:

Thecleaningsolutionmustbechosensothatthereactionisdriventotherightbecausethisputsthemetalionsinsolutionwheretheycanberinsedoff.Sincedrivingthereactiontotherightcorrespondstooxidation,weneedanoxidizingsolutiontocleanthewafer.

H2O/O2iscertainlyanoxidizingsolution.Butwhetheritcleanseffectivelyornotdependsonthestandardoxidationpotentialofthevariouspossiblereactions.FromTable4-3inthetext,wehave:

Oxidant/

Reductant

StandardOxidation

Potential（volts）

Oxidation-ReductionReaction

SiO2/Si

0.84

/Fe

0.17

/Cu

-0.34

/H2O

-1.23

/Au

-1.42

Thestrongerreactions（dominating）areatthebottom.

ThustheH2O/O2reactionwillcleanFeandCu,butitwillnotcleanAuoffthewafer.

4.5.ExplainwhyitisimportantthatthegenerationlifetimemeasurementillustratedinFigure4-19isdoneinthedark.

Answer:

Themeasurementdependsonmeasuringcarriersgeneratedthermallyinthesiliconsubstrate（oratthesurface）.Iflightisshiningonthesample,thenabsorbedphotonscanalsogeneratetherequiredcarriers.Asaresult,theextractedgenerationlifetimewiththelightonwouldreallybemeasuringtheintensityoftheincidentlightandnotabasicpropertyofthesiliconmaterial.

5.1.CalculateandplotversusexposurewavelengththetheoreticalresolutionanddepthoffocusforaprojectionexposuresystemwithaNAof0.6（aboutthebestthatcanbedonetoday）.Assumek1=0.6andk2=0.5（bothtypicalvalues）.Considerwavelengthsbetween100nmand1000nm（DUVandvisiblelight）.）.Indicatethecommonexposurewavelengthsbeingusedorconsideredtodayonyourplot（g-line,i-line,KrFandArF）.WillanArFsourcebeadequateforthe0.13µmand0.1µmtechnologygenerationsaccordingtothesesimplecalculations?

Answer:

Therelevantequationsaresimply

Theseequationsareplottedbelow.NotethattheArF（193nm）willnotreach0.13µmor0.1µmresolutionaccordingtothesesimplecalculations.Infact,withmoresophisticatedtechniquessuchasphaseshiftmasks,offaxisilluminationetc.,ArFisexpectedtoreach0.13µmandperhapsthe0.1µmgenerations.

5.3.AnX-rayexposuresystemusesphotonswithanenergyof1keV.Iftheseparationbetweenthemaskandwaferis20µm,estimatethediffractionlimitedresolutionthatisachievablebythissystem.

Answer:

Theequivalentwavelengthof1keVx-raysisgivenby

X-raysystemsoperateintheproximityprintingmode,sothatthetheoreticalresolutionisgivenbyEqn.5.12:

5.8.Asdescribedinthischapter,therearenoclearchoicesforlithographysystemsbeyondopticalprojectiontoolsbasedon193-nmArFeximerlasers.Onepossibilityisanopticalprojectionsystemusinga157-nmF2excimerlaser.

a.Assuminganumericalapertureof0.8andk1=0.75,whatistheexpectedresolutionofsuchasystemusingafirstorderestimateofresolution?

b.Actualprojectionsforsuchsystemssuggestthattheymightbecapableofresolvingfeaturessuitableforthe20090.07µmgeneration.Suggestthreeapproachestoactuallyachievingthisresolutionwiththesesystems.

Answer

a）.Thesimpleformulaforresolutionis

b）.Thecalculatedresolutioninpartaisafactoroftwolargerthanrequiredforthe0.07µmgeneration.Thereforesome“tricks”willhavetobeusedtoactuallyachievesuchres