Diffusion

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:Asanimpuritydopingmethod—lessimportantthanbefore;itisreplacedbyionimplantinICfabricationAsaneffectinjunctionanddevicestructureformationprocess—stillimportantCombinationofimplantanddiffusionMaintechniquefordopingengineeringofSiICdevicesAdvantageandproblemofdiffusionDiffusiondoping---nodamagecreatedasitinionimplantationDiffusiondopinglimitedtosolidsolubilityanddifficultyincontrollingimpurityprofileSomewordsofWilliamG.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.positions–Frequencyofatomvibration)exp(kTEZfmm2.Substitutionaldiffusion(替位扩散机制)VacancydiffusionExchangepositionsbetweenvacancyandimpurityatomSubstitutionaldiffusiondependsontwofactors:Avacancy(calledalsoShottkydefect)attheneighboringpositionImpurityatomhasenoughenergytoovercomethepotentialbarrier(Ea)*ConcentrationofSchottkydefectsatcertainTincrystalbystatistics:N–NumberofLatticePositionsEs--ActivationEnergyofSchottkyDefectsTheprobabilityofalatticepositionbeingavacancy*Theprobabilityforanimpurityatomtojumpformonelatticepositiontoanothercanbeexpressedby(v–Frequencyofatomvibration))exp(kTENnss)exp(kTENnss)exp(0kTE*TotalprobabilityforanimpurityatomtocompleteatranslationZ--Numberofneighbors(Z=4forSi))exp()exp()exp(kTEEzkTEkTEzfsosomoEE~msoEEEmffIsDD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:--byjumpmotionbetweentetrahedralsiteofspacingdForSilattice,eachlatticesitehasfourtetrahedralsituatedneighborsAsinglejumphasprojectionsoflengthd/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Diffusionfluxdensity:Diffusioncoefficient:,3/21dNNxNxNfdAtn62;62xNDxNfdj62fdDsec);/)(exp(6462022cmkTEEdfdDs)exp(4kTEEfso)exp(kTEDDAo→232dDo,soAEEEII.DiffusionEquationandDistributionofImpurities1.Fick’sLaw&diffusionequationFick’sfirstlaw:(FluxConcentrationgradient)F–Diff.flux(atoms/cm2sec)N–ImpurityconcentrationD–Diff.coef.ofimpurity(cm2/sec)xNDFDgradNFFick’ssecondlaw:ThenetflowofatomsintothevolumeisOrtNxAFFA)()(210FdivdtdN(ContinuityEquation)tNxFxFxFF21tNxNDx)(;or)(gradNDdivdtdN(Fick’ssecondlaw)tNxND22(Diff.Equation)Assumptionsmadeforthisequation:*NoElectricFieldEffect*DindependentofConcentration2.DiffusioncoefficientEA–ActivationenergyD0–Diffusionconstant(cm2/sec)(EAcorrespondstoformvacancyforsubstitutionaldiffusers)Diffusivitydepends