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SemiconductorMicrochipsandFabrication

IEEEPress

445HoesLane

Piscataway,NJ08854

IEEEPressEditorialBoard

SarahSpurgeon, EditorinChief

JónAtliBenediktsson

AnjanBose

AdamDrobot

Peter(Yong)Lian

AndreasMolisch

SaeidNahavandi

JeffreyReed

ThomasRobertazzi

DiomidisSpinellis

AhmetMuratTekalp

SemiconductorMicrochipsandFabrication

APracticalGuidetoTheoryandManufacturing

YaguangLian

UniversityofIllinois Urbana,USA

PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.

PublishedsimultaneouslyinCanada.

Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinany formorbyanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise, exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,without eitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentofthe appropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers, MA01923,(978)750-8400,fax(978)750-4470,oronthewebatwww.copyright.com.Requeststo thePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley& Sons,Inc.,111RiverStreet,Hoboken,NJ07030,(201)748-6011,fax(201)748-6008,oronlineat http://www.wiley.com/go/permission.

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Setin9.5/12.5ptSTIXTwoTextbyStraive,Chennai,India

Contents

AuthorBiography xi

Preface xiii

1IntroductiontotheBasicConcepts 1

1.1WhatIsaMicrochip? 1

1.2Ohm’sLawandResistivity 1

1.3Conductor,Insulator,andSemiconductor 5 References 5

2BriefIntroductionofTheories 7

2.1TheBirthofQuantumMechanics 7

2.2EnergyBand(Band) 11 References 15

3EarlyRadioCommunication 17

3.1TelegraphTechnology 17

3.2ElectronTube 19 References 22

4BasicKnowledgeofElectricCircuits(Circuits) 23

4.1ElectricCircuitsandtheComponents 23

4.2ElectricField 26

4.3MagneticField 28

4.4AlternatingCurrent 30

5FurtherDiscussionofSemiconductorsandDiodes 33

5.1SemiconductorEnergyBand 33

5.2SemiconductorDoping 36

5.3SemiconductorDiode 42 References 46

6TransistorandIntegratedCircuit 47

6.1BipolarTransistor 47

6.2JunctionFieldEffectTransistor 49

6.3Metal–SemiconductorFieldEffectTransistor 52

6.4Metal–Insulator–SemiconductorFieldEffectTransistor 55 References 60

7TheDevelopmentHistoryofSemiconductorIndustry 61

7.1TheInstructionofSemiconductorProductsandStructures 61

7.2ABriefHistoryoftheSemiconductorIndustry 63

7.3ChangesintheSizeofTransistorsandSiliconWafers 65

7.4CleanRoom 67

7.5PlanarProcess 71 References 75

8SemiconductorPhotonicDevices 77

8.1Light-EmittingDevicesandLight-EmittingPrinciples 77

8.2Light-EmittingDiode(LED) 82

8.3SemiconductorDiodeLaser 88

8.3.1ResonantCavity 89

8.3.2ReflectionandRefractionofLight 91

8.3.3HeterojunctionMaterials 93

8.3.4PopulationInversionandThresholdCurrentDensity 94 References 96

9SemiconductorLightDetectionandPhotocell 97

9.1DigitalCameraandCCD 97

9.2Photoconductor 100

9.3TransistorLaser 101

9.4SolarCell 105 References 106

10ManufactureofSiliconWafer 109

10.1FromQuartziteOretoPolysilicon 110

10.2ChemicalReaction 113

10.3PullSingleCrystal 115

10.4PolishingandSlicing 116 References 123

11BasicKnowledgesofProcess 125

11.1TheStructureofIntegratedCircuit(IC) 125

11.2ResolutionofOpticalSystem 128

11.3WhyPlasmaUsedintheProcess 131 References 133

12Photolithography(Lithography) 135

12.1TheStepsofLithographyProcess 135

12.1.1Cleaning 135

12.1.2DehydrationBake 136

12.1.3PhotoresistCoating 138

12.1.4SoftBake 141

12.1.5AlignmentandExposure 141

12.1.6Developing 145

12.1.7Inspection 146

12.1.8HardBake 147

12.1.9Descum 148

12.2AlignmentMark(Mark)DesignonthePhotomask 152

12.3ContemporaryPhotolithographyEquipmentTechnologies 156 References 159

13DielectricFilmsGrowth 161

13.1TheGrowthofSiliconDioxideFilm 162

13.1.1ThermalOxidationProcessofSiO2 162

13.1.2LTOProcess 164

13.1.3PECVDProcessofSiliconDioxide 166

13.1.4TEOS + O3 DepositionUsingAPCVDSystem 167

13.2TheGrowthofSiliconNitrideFilm 168

13.2.1LPCVD 168

13.2.2PECVDProcessofSiliconNitride 171

13.3AtomicLayerDepositionTechnique 174 References 177

14IntroductionofEtchingandRIESystem 179

14.1WetEtching 179

14.2RIESystemforDryEtching 182

14.2.1RIEProcessFlowandEquipmentStructure 182

14.2.2ProcessChamber 184

14.2.3VacuumPumps 186

14.2.4RFPowerSupply(Source)andMatchingNetwork(Matchwork) 187

14.2.5GasCylinderandMassFlowController(MFC) 189

14.2.6HeaterandCoolant 194

References 196

15DryEtching 197

15.1TheEtchProfileofRIE 197

15.1.1Case1 198

15.1.2Case2 201

15.2EtchingRateofRIE 203

15.3DryEtchingofIII–VSemiconductorsandMetals 206

15.4EtchProfileControl 207

15.4.1InfluenceofthePROpeningShapeontheEtchProfile 208

15.4.2TheEffectofCarbononEtchingRateandProfile 209

15.5OtherIssues 211

15.5.1TheDifferencesBetweenRIEandPECVD 211

15.5.2TheDifferenceBetweenSiandSiO2 DryEtching 214

15.6InductivelyCoupledPlasma(ICP)TechniqueandBoschProcess 215

15.6.1InductivelyCoupledPlasmaTechnique 216

15.6.2BoschProcess 219

References 223

16MetalProcesses 225

16.1ThermalEvaporationTechnique 225

16.2ElectronBeamEvaporationTechnique 227

16.3MagnetronSputteringDepositionTechnique 231

16.4TheMainDifferencesBetweenElectronBeam(Thermal)Evaporation andSputteringDeposition 234

16.5MetalLift-offProcess 235

16.6MetalSelectionandAnnealingTechnology 241

16.6.1TheSelectionofMetals 241

16.6.2MetalAnnealing 242

References 243

17DopingProcesses 245

17.1BasicIntroductionofDoping 245

17.2BasicPrinciplesofDiffusion 246

17.3ThermalDiffusion 247

17.4DiffusionandRedistributionofImpuritiesinSiO2 248

17.5MinimumThicknessofSiO2 MaskingFilm 250

17.6TheDistributionofImpuritiesUndertheSiO2 MaskingFilm 251

17.7DiffusionImpuritySources 252

17.8ParametersoftheDiffusionLayer 255

17.9Four-PointProbeSheetResistanceMeasurement 256

17.10IonImplantationProcess 257

17.11TheoreticalAnalysisofIonImplantation 259

17.12ImpurityDistributionafterImplantation 260

17.13TypeandDoseofImplantedImpurities 262

17.14TheMinimumThicknessofMaskingFilm 263

17.15AnnealingProcess 264

17.16BuriedImplantation 266

17.16.1ImplantationthroughMaskingFilm 266

17.16.2SOIManufacture 267

References 270

18ProcessControlMonitor,Packaging,andtheOthers 271

18.1DielectricFilmQualityInspection 271

18.2OhmicContactTest 273

18.3Metal-to-MetalContact 274

18.4ConductiveChannelControl 277

18.5ChipTesting 278

18.6Dicing 279

18.7Packaging 280

18.8EquipmentOperationRange 281

18.9Low-k andHigh-k Dielectrics 282

18.9.1CopperInterconnectionandLow-k Dielectrics 283

18.9.2QuantumTunnelingEffectandHigh-k Dielectrics 286

18.10End 291

References 293

Index 295

AuthorBiography

YaguangLian isaresearchengineerinHolonyak Micro&NanotechnologyLabattheUniversityof IllinoisatUrbana-Champaign(UIUC).In1979,he studiedattheDepartmentofElectronics,Hebei University,China.In1983,withabachelor’s degree,heworkedonsiliconepitaxyforasemiconductorcompanyfortwoyears.Yaguangreturned toHebeiUniversityasagraduatestudentin1985. In1988,hegothismaster’sdegree.From1988 to2001,heworkedwithHebeiSemiconductor ResearchInstitute(HSRI).In2001,Yaguang joinedastart-upcompanyatCaliforniaasasenior semiconductorprocessengineer.Twoyearslater, heworkedintheUniversityofCalifornia,LosAngeles(UCLA).FromNovember 2004tillnow,YaguangworksasresearchengineerattheUniversityofIllinois.

Withover35yearsofexperienceinthesemiconductorfield,Yaguanghas dealtwithdifferentprocessesfordifferentkindsofsemiconductors,suchasSi andGaAs.WhenheworkedinHSRIinChina,hewasmanufacturingGaAs MESFETdigitalICanddesigningcircuits,andalsomanagedaprocessflowfrom implantationtopackaging.InthecompanyatCalifornia,heworkedmainlyin themanufactureofsiliconopticalwaveguide.AtUCLA,Yaguangstartedthe equipmentrepairandmaintenance,andusers’training,whichhefurtherevolved atUIUC.Heisalsoresponsiblefordesigningdifferentrecipestomeettheneeds ofprofessorsindifferentprojects,suchasdryetchingofsilicon,III–Vmaterials, dielectricfilmsandmetals,anddepositionofsiliconnitridefilmwithdifferent

xii AuthorBiography

stresses.Hesolvesdifferenttypesofprocessproblemsforstudentspavingwayfor theirresearch.

Yaguangbelievesthattobeagoodengineer,onemusthaveanimportanttrait, whichis“itisnotenoughforyoutoknowhowtodoit,youmustknowwhy todoit.”

Preface

“Semiconductorprocessengineer”isthelabelofmywholecareer.Asaresearch engineer,IhavebeenworkinginHolonyakMicro&NanotechnologyLaboratory (HMNTL)attheUniversityofIllinoisfornearlytwodecades.Thecorepartof HMNTListhecleanroomwithdifferenttypesofequipment,whichareused tofabricatevarioussemiconductordevices.Thelabisopentothecampusand society.Uptonow,Ihavetrainedthousandsofusersinusingthelabmachines. Mostusersaredoctoralstudents.Thesetrainingexperienceshavegivenmethe opportunitiestoencountervariousissuesandsolvedifferenttechnicalproblems withdifferentkindsofusers.

Duringmyyearsoftraining,Ihavemetstudentswithdifferentbackgrounds. MostofthemhaveEEorECEbackgrounds,andsomeofthemdon’thavethese backgrounds.ThestudentwithoutEEorECEbackgroundslackbasicknowledge ofsemiconductorsandprocessing,whilestudentsmajoringinEEorECEneedto makeuptheworkingprinciplesofmanufacturingprocessesandthebasicstructuresofequipment.Lackofadequateunderstandingofprocessandequipment notonlyoccursinmanydoctoralstudentswithbackgroundsinEEorECE,but alsoinsomepostdoctoralresearchers.Animportantreasonforthisphenomenon isthattheydonotunderstandtheprocessandequipmentfromtheperspective ofphysicalandchemicalprinciples.Theseissuesandtheencouragementfrom studentsdrovemetowritethisbook.

Weareusingmicrochipstodescribesemiconductordevicesandintegrated circuits(ICs).TomeettheneedsofreaderswithoutEEorECEbackgrounds, thisbookincludestheknowledgeofsemiconductorconcepts,theories,histories, andbasicstructuresofmicrochips,whichhelptolaythefoundationforthemto understandsemiconductormanufacturingprocesses.Tohelpthereaderswith EEorECEbackgroundsbetterunderstandtheprocessandequipment,thisbook strivestoclarifytheprinciplesofprocesses,thebasicstructuresofequipment,and thedesignofprocessrecipesbasedonthephysicallaws,chemicalreactions,and electricalcircuittheories.Itnotonlyshowsreadershowtodotheprocess,but alsoexplainswhytheprocessisdesignedinsuchaway.Itcombinestheprocesses

Preface

withtheactualmachinesusedinthecleanroomattheUniversity.Therefore,the bookwillbeveryusefulforreaderswithdifferentbackgrounds.

Thisisahandybookformanyaudiencesasitstartswiththebasicconcepts anddailyexamples.Itusessimplelanguagetoexplaincomplicatedconcepts andtheories.Theneedsofvariouslevelsofaudienceswillbesatisfied,suchas undergraduates,graduates,researchers,engineers,andprofessors.Thebookwill pavethewaysforreadersintheirsemiconductorresearch,process,andmanufacture.Fromthisbook,readerscanfindmanyvaluablesuggestionsandsolutions totheproblemsthatstudentsorengineersoftenencounterinsemiconductor processing.Thesesuggestionsandsolutionsarebasedonmyyearsofworking experience.Moreover,readerscanalsofindsomeusefulexperimentalresultsin thebook,whichwillhelpthemintheirprocessingwork.

Nowadays,semiconductorsarewidelyusedinmanyfields.Thisbookis alsowrittenforthosewhoarenotmajoringbutinterestedintheresearchand productionofsemiconductormicrochips.Eventhosewhodonothaveenough knowledgeofsemiconductorandprocesses,aslongastheyhavebasicknowledge ofphysics,chemistry,andcircuit,afterreadingthisbook,caneasilylearnand quicklygrasptheprinciples,knowledge,andmanufacturingprocessesofsemiconductors.Fromthisbook,readerscanobtainthefundamentalconceptsand skills,whichwillbeanecessityinthedevelopmentofsemiconductorprocessing. Theycanapplyalltheseconceptsandskillsinsemiconductortechnologyto improvetheirproductqualityortheprojectresearch.

IcouldnotaccomplishmybookwithoutHMNTL.InHMNTL,Ihavegotten agoodtimewithmycolleagues.Iwouldliketoexpressmyappreciationtomy excellentcolleagues:Mr.JohnHughes,Dr.MarkMcCollum,Dr.EdmondChow, Dr.GlennysMensing,KenTarman,HalRomans,MichaelHansen,Lavendra Mandyam,KarthickJeganathan,PaulDiPippo.Fromthem,Ihavelearnedmore aboutthelayoutandmanagementofthecleanroomattheuniversity.Fromthem, Ialsohavegottenalotofhelpintheequipmenttroubleshooting,recipedesign,and parametertesting.IamsogladthatIhaveworkedwiththemforsomanyyears.

Inwritingthisbook,manyfriendshaveofferedtheirsupport.Dr.RuijieZhao gavemegoodadviceatthebeginning.Dr.WenjuanZhureviewedthedraft. Dr.AnmingGaopushedmetowritethebook.Mr.RamanKumarandAlvin Floresprovidedmegoodsuggestionsonsometheoreticalissues,andsome studentssuppliedmewithniceimages.IespeciallythankTianyiBai,mynephew, agraduatestudentattheUniversityofPennsylvania,whohasgivenmevaluable opinionsinsomeareas.Finally,IwouldliketothanktheInternet,whichwas bornfromsemiconductortechnology.FromtheInternet,Icaneasilyfindthe informationIneed.Here,Ideeplyappreciatethecompaniesandindividualswho agreedtoletmeusetheirimagesinthebook.

February12,2022 YaguangLian

UniversityofIllinoisatUrbana-Champaign Champaign,IL

IntroductiontotheBasicConcepts

1.1WhatIsaMicrochip?

Lookingbackonthedevelopmenthistoryofhumansociety,ithasgonethrough differentstagesofcivilization,fromtheprimitivestoneagetothemoderninformationage.Thematerialusedtosupportstoneagewasstone.Thematerialused tosupportinformationageissemiconductor.Socontemporarysocietyisessentiallyasemiconductorerarepresentedbysilicon.Thiserabeganinthelate1950s andearly1960sintheBayAreaofNorthernCalifornianearSanFranciscointhe UnitedStates.Later,peoplecalledthisarea“SiliconValley,”thesignofhightechnology(abbreviatedtohigh-tech),whichhavebroughtusintotheinformationage. Siliconandothersemiconductorsarethecornerstoneofthisera.Ifpetroleumis thoughtasthebloodofmodernsociety,semiconductormicrochipscanberegarded asthebrain.Semiconductortechnologyhasbeenintegratedbydifferentindustriestoenhancetheirtechnicallevel,andithasalsocomeintoourhouseholds.A microchipisasemiconductordeviceoranintegratedcircuit(IC).AnICistomake alotoftinysemiconductordevicesontoasmallflatpieceofsemiconductor(adie).

1.2Ohm’sLawandResistivity

Duetomicrochipsareoperatedbyelectricity,sofirst,letusgettoknowwhatelectricityis,andhowelectricityworks.SeeFigure1.1.Itisavoltageconverterfora smallhouseholdelectronicproduct.Theexplanationofsometechnicalwordson theconverterarelistedasfollows:

● “VAC”means“VoltsAlternatingCurrent”

● “Hz-Hertz”isthefrequencyunit

● “W-Watt”istheunitofpower

● “mA”means“milli-Ampere.”“Ampere-A”istheunitofelectriccurrent(abbreviatedtocurrent)

SemiconductorMicrochipsandFabrication:APracticalGuidetoTheoryandManufacturing, FirstEdition.YaguangLian.

Figure1.1 Avoltageconverterforan electronicproduct.Source:Harman InternationalIndustries,Incorporated.

Amongthem,voltage,current,andwattarethethreebasicparametersusedto expressthecharacteristicsofelectricity.Anotherbasicparameterisresistance,we willtalkaboutitinOhm’slawbelow.

Electricityisthesetofphysicalphenomena.Aphysicalphenomenonreferstoa processthatdoesnotproducenewsubstances,suchasthemovementofobjects, thefreezingandboilingofwater,andsoon.Correspondingtothisisachemicalphenomenon,whichreferstoaprocessthatcanproducenewsubstances.We callthisprocessachemicalreaction,forexample,oxygenandhydrogengenerate waterthroughachemicalreaction.Thereisalsoanuclearphenomenon,which isbeyondthescopeofthisbookandwillnotbediscussed.Now,letusreturnto thetopicofelectricity.Electricityisgeneratedbythemotionofmatterthathasa propertyofelectriccharge.Anelectricchargecanbepositiveornegative.Positiveoneiscalled“positivecharge”andrepresentedby“+.”Negativeoneiscalled “negativecharge”andrepresentedby“ .”Themovementofelectricchargesis anelectriccurrent.Inmostcases,thecurrentisproducedbythemovementof electrons,whicharenegativecharges.Theunitofelectriccurrent,Ampere,is namedinhonorofaFrenchmathematicianandphysicistAndré-MarieAmpère (1775–1836),whoisconsideredthefatherofelectrodynamics.

Electricitycomesintoourhomesthroughelectricalwiresandthengoestovariouselectricalappliances.Thereareusuallytwokindsofelectricalwires(abbreviatedtowire)forhouseholduse.Theyaretwo-corewires,justlikethewireattached totheconverterinFigure1.1,andthree-corewires.Ifwestripathree-corewire, itsstructureisshowninFigure1.2.“CableJacket”istheinsulatingsheath,“Wire Insulation”istheinsulatinglayer,and“StrippedWire”isthewireexposedafter

Figure1.2 Thebasicstructureofthree-core wire.

theinsulatinglayerisstripped.Thethreewiresarehot,neutral,andground.Most oftheinsulatingsheathesandlayersaremadeofrubberandplastic;thewireis madeofmetal.Inmostcases,themetalisaluminumorcopper.Thekindofmaterialssuchasrubberandplasticarecalledinsulators,inwhich,electronscannot move.Thus,currentcannotflowintheinsulators.Wecallaluminumandcopper,thetypeofmaterials,conductors,becauseelectronscanmoveinthem.Thus, electricalcurrentcanflowintheconductors.

Allmaterialsarecomposedofatoms,andatomswillhinderthemovementof electrons,whichmeansthatallmaterialshaveresistanceintheoppositedirectionofthecurrentflow.Thisresistanceiscalledelectricalresistance(abbreviatedtoresistance),andtheunitoftheresistanceisOhm,whichisrepresentedby “Ω.” Ω isnamedinhonoroftheGermanphysicistGeorgSimonOhm(March16, 1789–July6,1854).Howdoelectronsmoveinaconductortogeneratethecurrent? Theyaredrivenbythepressureofelectricity.Thisspecialpressureiscalledvoltage, andtheunitisvolt,whichisexpressedby“V.”ThevoltageunitvoltistocommemoratetheItalianphysicistAlessandroVolta(1745–1827),whoinventedvoltaicpile, thefirstelectricalbatteryintheworld.Now,wehavethreeparametersrelated toelectricity:current,representedby“I ”;resistance,representedby“R”;voltage, representedby“V .”Sometimeslowercaselettersarealsousedtoindicatecurrent, resistance,andvoltage.TherelationshipbetweenthemisthefamousOhm’slaw:

Whycanelectronsflowinmetal?Itisbecausethemetalhaslittleresistance; electronscannotflowintheinsulatorbecausetheinsulatorhaslargeresistance. Scientistsuseresistivitytoexpresstheresistanceofamaterialperunitlength. “ ��”isusedtorepresentresistivity,itsunitisohm ⋅ cm(Ω ⋅ cm).Therelationship betweenresistanceandresistivityisexpressedbythefollowingformula:

Figure1.3 Adiagramofasectionofresistivematerial,currentﬂowsalongthelength direction.Source:ReproducedwithpermissionofPhysicsLibreTexts.

SeeFigure1.3,where“A”isthecross-sectionalarea,and“L”isthelengthof apieceofmaterial.Tomakemoreconvenientforpracticaluse,weintroducethe conceptofconductance.Thesymbolofconductanceis G,andtherelationship withresistance R isasfollows:

Theunitof G isSiemensandisrepresentedbytheletterStocommemorate WernervonSiemens(December13,1816–December6,1892).HewasaGerman scientistandfounderofSiemens.Correspondingly,thereisconductivity,expressed by �� ,andtherelationshipwithresistivity �� is

Inpracticalapplication,weoftenusedevicescalledresistors,whichareshown intheleftofFigure1.4,andthesymbolisshownintherightofFigure1.4.

Figure1.4 Thepictureofresistors(a)andthesymbol(b).Source:Reproducedwith permissionofSparkFunElectronics.

1.3Conductor,Insulator,andSemiconductor

Now,weuseresistivitytodistinguishconductorsandinsulators.Ingeneral,the resistivityofaconductorisverylow,andtheresistivityofaninsulatorisveryhigh. Forexample,theresistivityofcopperis1.55 × 10 6 Ω cm,andforaluminumis

2.5 × 10 6 Ω cm[1],where10 6 isonemillionth.Polyvinylchloride(PVC)isa kindofplasticcommonlyusedformakinginsulatingmaterials,itsresistivityis

2 × 1012 –2 × 1014 Ω ⋅ cm,nylonis4.56 × 1016 Ω ⋅ cm[2].Mathematically,102 means thereisazeroafter10,103 meanstherearetwozerosafter10,andsoon.From which,wecanknowthattheresistivityoftheabovetwoinsulatingmaterials has11–15zerosafter10.Conductorsandinsulatorshavetheresistivitieseither extremelysmallorextremelylarge.Doesamaterialwithresistivitybetweenthem exist?Yes,thismaterialexists,wecallitasemiconductor.Atroomtemperature,the resistivityofsiliconis6.3 × 104 Ω ⋅ cm,andtheresistivityofgermaniumis46 Ω ⋅ cm [1].SiliconwiththesymbolSiisthemostimportantmaterialinthemodern semiconductorindustry.ThatiswhytheBayAreaofNorthernCaliforniaiscalled SiliconValley.GermaniumwiththesymbolGewasusedtomakethefirsttransistorintheworld.Siliconandgermaniumaresingle-elementsemiconductors. Anotherkindofsemiconductorsarecompoundsemiconductors.Themostused oneisgalliumarsenidewithsymbolGaAs,whichhasaresistivityof107 –109 Ω cm [3].Withsuchahighresistivity,wecallthismaterialasemi-insulator.Duetothe highresistivity,pureGaAscannotbeusedtomakeadevice.Itmustbechanged toasemiconductorbyaprocessofdoping.Infact,siliconalsoneedstobedoped tomakedevices.WewilldiscussdopingprocessinChapter17.

Sofar,byusingtheresistivity,wehavedistinguishedbetweenconductors, semiconductors,semi-insulators,andinsulators.Generally,semi-insulating materialsrepresentedbyGaAsneedtobeconvertedintosemiconductorsbefore theycanbeusedtomakedevices.So,inthefollowingdiscussion,wewillclassify semi-insulatingmaterialsassemiconductors.Itistoosimpletodistinguish materialsfromresistivity.Toreallyunderstandthem,especiallysemiconductors, wehavetousequantummechanicsandenergybandtheory.Itisnecessaryforus togiveabriefintroductionofquantummechanicsandenergybandtheory.

References

1 饭田修一等,(1979). 物理学常用数表,[日]. 科学出版社,133–135.

2 Fink,D.G.andBeaty,H.W.(1987). StandardHandbookforElectricalEngineers, 12e,4–153.McGraw-HillCompanies.

3 Soares,R.,Graffeuil,J.,andObrégon,J.(1983). ApplicationsofGaAsMESFETs, 17.ArtechHouse.

Thischapterisabriefintroductionofquantummechanics,andthenenergyband theory.Byusingthesetheories,wecaneasilyunderstandwhatisaconductor,an insulator,andasemiconductor.

2.1TheBirthofQuantumMechanics

Attheendofthenineteenthcenturyandthebeginningofthetwentiethcentury,Newtonianmechanics,Maxwell’stheoryoftheelectromagneticfield,and Maxwell–Boltzmannstatisticsconstitutedwhatisnowcalledclassicalphysicsthat ruledthephysicalworldatthattime.Thephysicalquantitiesdiscussedinclassicalphysicshavetwocharacteristics:continuityandcontrollability.However,there weretwoproblemsthatcouldnotbesolvedbyusingthetheoryofclassicalphysics. Onewasblackbodyradiation,andtheotherwasMichelson–Morleyexperiment. In1900,MaxPlanck(April23,1858–October4,1947),aGermantheoreticalphysicistproposedthatintheradiationandabsorptionofelectromagneticfield,the energyappearedinadiscreteratherthancontinuousform.Thisdiscreteenergy iscalledthequantizationofenergy.Thisassumptionexplainsblackbodyradiationverywellandisconsideredasthebeginningofquantummechanics.In1905, AlbertEinstein(March14,1879–April18,1955)publishedthetheoryofspecialrelativitytoexplainMichelson–Morleyexperiment.Sincethen,physicshasentered thepost-Newtonianeraofmodernphysics.

AccordingtoPlanck’sassumption,eachpartofenergyisproportionaltothe frequencyofelectromagneticradiation.Weuse E torepresenttheenergyand �� to representthefrequency.ThePlank’sequationis

E = h��

(2.1)

The“h”hereiscalledPlanck’sconstant.Thefrequencyisthenumberofoccurrencesofarepeatingeventperunitoftime.Inmostcases,frequencyisrepresented

SemiconductorMicrochipsandFabrication:APracticalGuidetoTheoryandManufacturing, FirstEdition.YaguangLian.

bytheletter“f .”However,inquantummechanicsitisrepresentedby“ν.”“T ”is usedtorepresenttheperiod.Itisthedurationoftimeofonecycleinarepeating event.Therelationshipbetween f and T isasfollows:

Ifweusesecondstoexpresstime,thenunitoffrequencyisHertz(Hz),named afterGermanphysicistHeinrichHertz(February22,1857–January1,1894).He usedtheexperimenttoconfirmtheexistenceofelectromagneticwaves.ElectromagneticwavesweretheoreticallypredictedbyJamesClerkMaxwell(June13, 1831–November5,1879).Thetheoryiswell-knownasMaxwell’sequations.The experimentalsoprovedthatthelightiselectromagneticwavesthatwerepredicted byMaxwell.

Planck’sEq.(2.1)playsaveryimportantroleinphysics.Itisoneofkeydifferencesbetweenclassicphysicsandmodernphysics.Inclassicphysics,theenergyis supposedtoexistinthecontinuousformandisvalidatalarge(macroscopic)scale. ThePlanckequationpointsoutthatatsmall(microscopic)scale,energyexistsin thediscrete(quantum)form,whichisoneofthebasiccharacteristicsofquantum mechanics.Therefore,whendealingwithmicroscopicworldssuchasatomsand subatomicparticles,wemustusequantummechanics.

In1905,Einsteinpublishedfourpapers–photoelectriceffect,Brownianmotion, specialtheoryofrelativity,andmass–energyequivalence.Thesefourarticlescontributedsubstantiallytothefoundationofmodernphysicsandchangedpeople’s viewsfrombeginningofhistoryonspace,time,mass,andenergy.Sothisyearis alsocalledthe“miracleyear”ofphysics.Inthepaperofmass–energyequivalence, Einsteinwrotedownawell-knownequation:

Inthisequation, E isenergy, m ismass, c isthespeedoflight, c = 300000km/s. Now,letustalkaboutphotoelectriceffect.Theeffectmeansthatwhenlight beamsshineonthesurfaceofanobject(mostlymetal),andifthelightfrequency ishigherthanacertainnumber,theelectronsonthesurfacewillbeexcited andescapefromtheobject.ThisphenomenonwasfirstdiscoveredbyHertz. Theescapedelectronsarecalledphotoelectrons.Inthepaperofphotoelectric effect,Einsteinassumedthatlighttravelthroughspace,notintheformofwaves asdescribedintheclassicaltheoryofelectromagneticfield,butindiscrete “wavepackets.”Awavepacketiscalleda“photon.”AphotonobeysPlanck’s equationandhasenergyof h�� .Whenthefrequency(energy)ofphotonsthatare illuminatingtheobjectreachesorexceedsacertainthresholdfrequency,electrons willbeemittedoutofthesurfaceoftheobject(seeFigure2.1).

In1913,NielsBohr(October7,1885–November18,1962),aDanishphysicist, andErnestRutherford(August30,1871–October19,1937),aBritishphysicistborn

E = mc2

(2.3)

Figure2.1 Theschematicdiagramofphotoelectriceffect.Source:Reproducedwith permissionofScienceABC.WhatisthePhotoelectricEffect? ≫ ScienceABC.

inNewZealand,togetherproposedamodeltodescribeatoms.Thismodelstates thatanatomcontainssmall,high-densitynucleus,surroundedbyelectrons.This islikethestructureofthesolarsystem,exceptthatthisattractioncomesfromelectromagneticforceratherthangravity.WecallthismodelRutherford–Bohrmodel, orsimplyBohrmodel.Figure2.2isBohrmodelofahydrogenatom.Inthisfigure, thenucleusisinthecenter,whichiscomposedofaneutronandaproton.Anelectronrotatesinouterorbits.Neutronisunchargedandprotonispositivelycharged. Sincethenumberofprotonsinanatomisthesameasthenumberofelectrons,

Figure2.2 Bohrmodelofahydrogenatom.(a)Aphotonisabsorbedandanelectron jumpsfromaninnerorbittoanouterorbit.(b)Anelectronjumpsfromanouterorbitto aninnerorbitandaphotonisemitted.Source:[1]Bertolotti/Taylor&Francis.

2BriefIntroductionofTheories

undernormalcircumstances,theatomisnotchargedandisneutral.Thehydrogen atomiscomposedofanucleusandanelectron.

Inthismodel,theelectronisusuallyonaninnerorbit.Thisorbithasthelowest energyandiscalledthegroundstate(level).Butwhentheelectronabsorbsenough energy,itjumpstoanouterorbit(higherenergy),asshowedin(a).Theouter orbitiscalledanexcitedstate.Theexcitedstatecanhavemanystateswithdifferentenergyorbits,andwhichorbittheelectronjumpstodependsonhowmuch energyitabsorbs.Theelectronisunstableintheexcitedstates.Itwilljumpback tothelowerenergyorbitandreleaseitsenergybyemittingaphoton,asshowedin (b).Sometimes,wecanuse ΔE = h�� torepresenttheemittedphoton.“Δ”usually meansdifferenceinmathematics.Figure2.3isaschematicdiagramoftheenergy levelsofasiliconatom.Siliconiscomposedof1nucleusand14electrons.The nucleuscontains14protonswithpositivecharge.The“shell”inthefiguremeans thattheelectronsmovesofastthatanelectroncloudisformedaroundthenucleus, justlikeashell.Valenceelectronsaretheelectronslocatedinoutermostorbit.Ionizedlevelreferstoastatewhereanelectronhasabsorbedenoughenergytogetrid ofthebondageofthenucleusandbecomeafreeelectron.Inthiscase,theneutralityofanatomisbroken.Theremainingatombecomespositivecharge.Such atomsarecalledpositivelychargedions(positiveions).Theelectronsinphotoelectriceffectareionizedelectrons.Asmentionedabove,electronstendtooccupy thelow-energylevels,whicharetheshell1andshell2asshowninthefigure.They aretheinnershells.Theelectronsfullyoccupythestatesinthesetwoshells.The

Figure2.3 Bohrmodelofasiliconatom.Source:Adaptedfrom“HyperPhysics”of GeorgiaStateUniversity.

2.2EnergyBand(Band) 11

electronsatthesetwolevelsarestable.Inshell3,thenumberofelectronsisless thanthenumberofstatesinthislevel,soelectronscannotcompletelyoccupythe states.Theelectronsinthislevelarevalenceelectronsthatdeterminethechemicalpropertiesofsubstance.Theyparticipateinchemicalreactionandareeasily excitedtohigher-energystates.Siliconhasfourvalenceelectrons,andgermanium alsohasfour.

BasedontheworksofPlanck,Einstein,andBohr,ErwinSchrödinger(August 12,1887–January4,1961),anAustrianphysicist,publishedSchrödingerequation in1926.Sofar,quantummechanicshadbeeninitiallyestablished.

2.2EnergyBand(Band)

ThephotoelectriceffectandBohrmodelimplyanimportantcharacteristicofelectrons,thatis,theyonlyoccupysomespecialenergylevels.Inthecaseofasingle atom,theseenergylevelsarediscrete.Butinacrystalmaterial,suchassilicon, discreteenergylevelsbecomeenergybands.Matterusuallyhasthreestates,solid, liquid,andgas.Thebranchofphysicsthatisthestudyofsolidsiscalledsolid-state physics.Ifasolidhasaperiodicandrepeatingstructure,itisacrystallinesolid (singlecrystalmaterial).Thesemiconductorsweareusingtomakemicrochips aremainlycrystallinesolids.Siliconhasasingle-atomstructure.Insiliconcrystals,atomsarearrangedperiodicallyandorderly.Figure2.4isaschematicdiagramofsiliconcrystalstructure.Thesmallballsinthefigurerepresentsilicon atoms,and X –Y –Z isthecoordinatesystem.Becausetheatomsareveryclosein thecrystal,thevalenceelectronsinanatomappeartobesharedbyotheratoms. Therefore,thediscreteenergylevelsofelectronsinasingleatombecomeenergy

Figure2.4 Schematic diagramofasilicon crystal.

bandsinacrystalmaterial.Usingthisviewandextendingquantummechanicsto solid-statephysics,oneoftheresultsobtainedisenergybandtheory.Bysolving theSchrödingerequation,thebandstructuresofdifferentcrystallinesolidscan beobtained.

Differentcrystalmaterialshavedifferentenergybandstructures,buttheyall haveonethingincommon.Someenergybandsallowelectronstooccupy,and someenergybandsprohibitelectronstooccupy.Energybandsthatprohibitelectronicoccupationarecalledforbiddenbands.Energybandsthatallowelectronic occupationaredividedintotwocategories:valanceband(fullband)andconductionband(emptyband).Accordingtothetheoryofsolid-statephysics,adjacent atomssharevalenceelectrons(Figure2.3).Apairofvalenceelectronsformabond. Thisisacovalentbond.Asmentionedabove,inasolid,thediscreteenergylevels becomeenergybands.Theenergybandiscomposedofmassiveenergylevels withsubtledifferences.Forvalenceelectrons,thischangeiscausedbytheenergy levelsplittingofthevalenceelectrons.Inthestructureofenergyband,theband generatedbytheenergylevelsplittingofthevalenceelectronsiscalledthevalence band.Ifthevalencebandisfilledwithelectrons,thisbandiscalledfullband. Similarly,anexcitedstateenergylevelwillsplittoformanexcitedstateenergy band.Iftherearenoelectronsinthisexcitationband,thebandiscalledempty band.Undercertainconditions,somevalenceelectronswillbeexcitedtotransit intothisband,andtheseelectronswillgenerateelectriccurrent.Atthistime,the bandiscalledconductionband.Inmostcases,wedonotmentionfullbandand emptybandseparatelybutclassifythemasvalencebandandconductionband. Bandtheoryandbandstructureclearlyshowthedifferencebetweenconductors,insulators,andsemiconductors.Figure2.5isaschematicdiagramofthe energybandstructureofthesematerials.Inthisfigure,wecanseevalenceband, conductionband,andbandgap.Bandgapisalsocalledtheforbiddenband.

Figure2.5 Schematicdiagramoftheenergybandstructureofasolid[2].Source: ChineseTechnicalBooks.(a)Valenceandconductionbandsoverlap(b)Valencebandis notfull(c)Bandgapisbig(d)Bandgapissmall.

Thefigureshowsthatelectronsareintheconductionbandandholesarein valenceband.InFigure2.5a,thetopofvalencebandoverlapswiththebottomof conductionband.Thereisnoforbiddenband.Manyelectronsautomaticallyreach theconductionbandandparticipateinconduction.Thisisatypeofconductor. Calciumisanexampleofsuchconductor.InFigure2.5b,althoughthereisalarge forbiddenband,thevalencebandisnotfull,andelectronscaneasilyflowin thevalencebandtoparticipateinconduction.Thisisanothertypeofconductor, andcopperisoneexampleofthiskindofconductor.Soaccordingtoenergy bandtheory,therearetwotypesofmetals.Figure2.5cisaschematicdiagram oftheenergybandofaninsulator.Thisstructurehasaverylargeforbidden band.Undernormalcircumstances,electronscannotreachtheconductionband. Theconductionbandisbasicallyanemptyband,whilethevalencebandisfull. Noelectronicflow,noelectriccurrentisgenerated.Figure2.5disaschematic diagramofthesemiconductorenergyband.Thisenergybandhasaforbidden band,buttheforbiddenbandisverynarrow.Atroomtemperature,someofthe electronsinthevalencebandwilltransitfromthevalencebandtotheconduction bandthroughthermalexcitation.Thetransitionofelectronswillleavesome vacanciesinthevalenceband,whichareholesmentionedabove.Aholeis positivecharge.Theelectronsenteringtheconductionbandwillparticipatein conduction,andtheholesremaininginthevalencebandwillalsoparticipatein conduction.

Fromtheenergybandtheory,wecanclearlyseethedifferencebetweenconductors,insulators,andsemiconductors,aswellasthedifferenceofelectricconductionbetweenconductorsandsemiconductors.Inaconductor,onlyelectrons contributeelectriccurrent.Inasemiconductor,electronsandholescontribute electriccurrent.Althoughsemiconductorshavetwotypesofchargedparticles (positiveandnegative)thatparticipateinconductionatthesametime,sincethe totalchargedparticleconcentrationislessthantheconcentrationofelectronsin theconductor,theconductivityofthesemiconductorissmallerthanthatofthe conductor.Inotherwords,theresistivityofthesemiconductorisbiggerthanthat oftheconductor.

Weknowthatelectriccurrentisgeneratedbythemovementofelectriccharges drivenbyvoltage.Inasemiconductor,themovementofelectronsandholescreate thecurrent.However,theirmovementvelocitiesaredifferent.Weusemobilityto furtherdescribethisvelocity.Mobilityisdefinedashowfastchargecarrierslike electronsmoveinasemiconductordrivenbyvoltage. �� isusedtoexpressmobility. WewilldiscussitmoreinChapter5.

InChapter1,wesaidthatatomswouldhinderthemovementofelectronsand generateresistance.Wealsosaidbeforethatifthestructureofasolidisperiodicallyandorderly,thissolidisacrystallinematerial.Asolidiscomposedofatoms. Inordertovisualizethearrangementofatomsinacrystallinematerial,anatom canbesimplifiedintoonepoint,andthesepointscanbeconnectedbyimaginary