半导体工艺-复旦大学-蒋玉龙-Chapter09

Chapter9DiffusionOutlineI.DiffusionMechanism1.InterstitialDiffusion2.SubstitutionalDiffusion3.Interstitialcydiffusion4.SimplifiedmodelofdiffusivityII.DiffusionEquationandDistributionofImpurities1.Fick’sLaw&diffusionequation2.Diffusioncoefficient3.Predeposition(constantsurfaceconcentrationdiffusion)4.Drive-inDiffusion(constanttotaldopantdiffusion)III.DiffusionimpuritiesandsourcesIV.FieldaidedextrinsicdiffusionV.ConcentrationdependenceandatomisticmodelofdiffusionVI.DiffusioncoefficientanddepthprofileofB,As,PVII.OxidationeffectondiffusionVIII.DiffusioninPolySiDiffusionasadopingmethod‹DiffusiontechniqueforsemiconductordevicewasinventedbyPfannin1952Pfann’spatent(1952)–DiffusiontechniqueforSi,Ge,toalterthetypeofconductivity‹DiffusionforULSItechnology:¾Asanimpuritydopingmethod—lessimportantthanbefore;itisreplacedbyionimplantinICfabrication¾Asaneffectinjunctionanddevicestructureformationprocess—stillimportant¾Combinationofimplantanddiffusion9MaintechniquefordopingengineeringofSiICdevices‹Advantageandproblemofdiffusion¾Diffusiondoping---nodamagecreatedasitinionimplantation¾DiffusiondopinglimitedtosolidsolubilityanddifficultyincontrollingimpurityprofileSomewordsofWilliamG.Pfann‹“Thecreationactisanephemeralthing,whichrequiresfirstofallhardworkandtotalabsorptionintheproject”‹“Creativityalsorequiresanuncannyabilitytoconnectdisparateideas.”‹“Isayuncannybecausetheprocesscertainlydoesnotappearlogical”‹“AndIsayephemeralbecausethere’sjustfleetingmoment,triggeredbyaccident,inwhichtheconnectionismade”“创造行为往往是瞬间发生的事,但它却需要对研究客体的艰苦工作和全面深入了解。”“创造性还需要一种能在不同思路间建立连接的奇异能力。”“我说‘奇异能力’，因为其过程往往显得不合逻辑。”“我说‘瞬间发生’，因为往往是在逝瞬间,偶然触发建立起那种连接。”I.DiffusionMechanism‹Interstitialdiffusion(Li,K,Na,Ar,H,…--I,VIIIGroupelementsinSi)‹Substitutionaldiffusion(B,P,As,Sb…)‹Diffusioncoefficient:DSDISiliconvacanciesarerequiredforsubstitutionaldiffusion,directexchangebetweenimpurityandSiatomswillneedhigherenergy1.Interstitialdiffusion(间隙扩散机制)‹Certaininterstitialpositionsincrystals,especiallytheimpuritywithsmalleratomicradiuscanoccupysuchinterstitialpositionsandmovefromonetoanotherneighboringinterstitialposition.‹Thereisanenergybarrierbetweentwointerstitialpositions(Em~1eV)‹Probabilityofaninterstitialatomtojump:Z–Numberofnearestneighborinter.positionsν–Frequencyofatomvibration)exp(kTEZfmm−=ν2.Substitutionaldiffusion(替位扩散机制)¾Vacancydiffusion¾ExchangepositionsbetweenvacancyandimpurityatomSubstitutionaldiffusiondependsontwofactors:¾Avacancy(calledalsoShottkydefect)attheneighboringposition¾Impurityatomhasenoughenergytoovercomethepotentialbarrier(Ea)*ConcentrationofSchottkydefectsatcertainTincrystalbystatistics:N–NumberofLatticePositionsEs--ActivationEnergyofSchottkyDefects∴Theprobabilityofalatticepositionbeingavacancy*Theprobabilityforanimpurityatomtojumpformonelatticepositiontoanothercanbeexpressedby(v–Frequencyofatomvibration))exp(kTENnss−=)exp(kTENnss−=)exp(0kTE−ν*TotalprobabilityforanimpurityatomtocompleteatranslationZ--Numberofneighbors(Z=4forSi))exp()exp()exp(kTEEzkTEkTEzfsoso+−=−−=ννmoEE~msoEEE+mff∴ÆIsDD∴3.Interstitialassisteddiffusion‹Combinedinterstitial-substitutionalmotion--AninterstitialSiatomdisplacesasubstitutionalimpurityatom,drivingittoaninterstitialsitewhereitdiffusessomedistancebeforeitreturnstoanextsubstitutionalsite.Therefore,theSiinterstitialsplayaroleincontrollingdiffusiontogetherwithSivacancies‹BandPatomsmaydiffusebybothsubstitutionalandinterstitialcymechanismsindependenceontheprocessingcondition;interstitialcydiffusionparticularlyimportantatT1000°CKick-outdiffusion（填隙式扩散）Interstitialcydiffusion（推填式扩散）4.Simplifiedmodelofdiffusivity(orcalleddiffusioncoefficient)*Forsubstitutionaldiffusion:--byjumpmotionbetweentetrahedralsiteofspacingd¾ForSilattice,eachlatticesitehasfourtetrahedralsituatedneighbors¾Asinglejumphasprojectionsoflengthd/31/2alongeachofthecrystalaxes*DiffusionduetoconcentrationgradientLayer1:n1–Numbersofimpurityatom,N1–ImpurityconcentrationLayer2:n2,N2Thenetflowofatomsacrosstheplanepinx-directionInasinglejumpperiodoftime1/f,1/2ofthemovingatomsjumprightwhiletheother1/2jumpleft,ontheaverage(f-probabilityforanimpurityatomtocompleteatranslation);311AdNn⋅⋅=AdNn⋅⋅=322;311AdnN=∴AdnN223=∴)(32/12/)(2121NNAdffnntn−=−=ΔΔDiffusionfluxdensity:Diffusioncoefficient:→−=ΔΔ,3/21dNNxNQxNfdAtnΔΔ−=ΔΔ∴62;62xNDxNfdj∂∂−=ΔΔ−=62fdD=sec);/)(exp(6462022cmkTEEdfdDs+−==ν)exp(4kTEEfso+−=ν)exp(kTEDDAo−=→232dDoν=,soAEEE+=II.DiffusionEquationandDistributionofImpurities1.Fick’sLaw&diffusionequation¾Fick’sfirstlaw:(Flux∝Concentrationgradient)F–Diff.flux(atoms/cm2sec)N–ImpurityconcentrationD–Diff.coef.ofimpurity(cm2/sec)xNDF∂∂−=DgradNF−=r‹Fick’ssecondlaw:¾Thenetflowofatomsintothevolumeis¾OrtNxAFFA∂∂Δ=−)()(210=+FdivdtdNr(ContinuityEquation)tNxFxFxFF∂∂=∂∂−≅ΔΔ−=Δ−∴21tNxNDx∂∂=∂∂−∂∂−∴)(;or)(gradNDdivdtdN=(Fick’ssecondlaw)tNxND∂∂=∂∂22(Diff.Equation)Assumptionsmadeforthisequation:*NoElectricFieldEffect*DindependentofConcentration2.DiffusioncoefficientEA–ActivationenergyD0–Diffusionconstant(cm2/sec)(EAcorrespondstoformvacancyforsubstitutionaldiffusers)‹Diffusivitydependso