EE143 – Ali JaveySection 7: DiffusionJaeger Chapter 4EE143 – Ali JaveySurface Diffusion: Dopant Sources(a) Gas Source: AsH3, PH3, B2H6(b) Solid SourceBN Si BN Si(c) Spin-on-glassSiO2+dopant oxide(d) Liquid Source.EE143 – Ali JaveyFick’s First Law of Diffusiont coefficiendiffusion =DxNDJ∂∂−=EE143 – Vivek Subramanian Slide 4-4Fick’s Second Law of Diffusiondevicesmodernin situationsmany in t trueisn'which t,independen-ionconcentrat is D Assumes Eqn. Continuity with LawFirst Combine :Diffusion of Law Second sFick' dimension) one(in flux particle theof divergence theof negative the toequal ision concentrat of increase of Rate:Flux Particlefor Equation Continuity22xNDtNxJtN∂∂∂∂∂∂∂∂=−=EE143 – Ali JaveyB,PAs10-6AuCukTEOAeDD−=Diffusion Coefficients of Impurities in SiSubstitutionalDiffusersInterstitialDiffusersEE143 – Ali JaveyDiffusion Coefficientsre temperatuabsolute=TJ/K x101.38=constant sBoltzmann'=kenergy activationEipRelationsh Arrhenius exp23-A=⎟⎠⎞⎜⎝⎛−=kTEDDAOEE143 – Ali Javey(a) Interstitial DiffusionDiffusion Mechanisms in Si 10-6cm2/secAuCuFast DiffusionExample: Cu, Fe, Li, HEE143 – Ali Javey(b) Substitutional Diffusion Diffusion Mechanisms in Si (c) Interstitialcy DiffusionExample: Dopants in Si ( e.g. B, P,As,Sb)EE143 – Vivek Subramanian Slide 4-9Constant Source DiffusionComplementary Error Function Profiles()()FunctionError ary Complement=erfctCoefficienDiffusion ionConcentrat Surface2, :Dose Total2, :ionConcentrat0000====⎟⎠⎞⎜⎝⎛=∫∞DNDtNdttxNQDtxerfcNtxNπEE143 – Ali JaveyLimited Source DiffusionGaussian Profiles()ProfileGaussian tCoefficienDiffusion ion Concentrat Surface2exp2exp, :ionConcentrat00220===⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛−=⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛−=DDtQNNDtxDtQDtxNtxNππEE143 – Ali JaveyTwo Step Dopant Diffusion (1) Predepositiondopant gasSiO2SiO2Sidose control(2) Drive-in Turn off dopant gasor seal surface with oxideSiO2SiO2SiSiO2Doped Si regionprofile control(junction depth;concentration)Note: Predeposition by diffusion can also be replaced by a shallow implantation step.Note: Predeposition by diffusion can also be replaced by a shallow implantation step.EE143 – Ali JaveyPredepositionPredepositionDrive-inDrive-inNormalized Concentration versus depthEE143 – Ali JaveyDiffusion of Gaussian Implantation ProfileEE143 – Ali Javey∑=istepieffectiveDtDtBudgetThermal)()(ExampleDttotalof :Well drive-inandS/D annealingTemp (t)timewelldrive-instepS/DAnnealstepTemp (t)timewelldrive-instepS/DAnnealstepFor a complete process flow, only those steps with high Dt values are importantFor a complete process flow, only those steps with high Dt values are importantSuccessive Diffusions: Thermal BudgetEE143 – Ali JaveySolid Solubility Limits• There is a limit to the amount of a given impurity that can be “dissolved” in silicon (the Solid Solubility Limit)• At high concentrations, all of the impurities introduced into silicon will not be electrically activeEE143 – Ali JaveyHigh Concentration Diffusion EffectsLog C(x)xLow conc profile:Erfc or gaussianLog C(x)xJ largeJ smallHigh conc. profile:D gets largerwhen C(x) is large * C(x) looks “flatter”at high conc. regions1) E-Field Enhanced Diffusion2) Charged point defects enhanced diffusionEE143 – Ali JaveyElectric-field EnhancementExample: Acceptor DiffusionNa(x)Na(x)=Na-(x)p(x)hole gradientxHole diffusion tendencyE build-inComplete acceptorionization at diffusion temperatureComplete acceptorionization at diffusion temperatureAt thermal equilibrium, hole current =0Hole gradient creates build-inelectric field to counteract the hole diffusion tendencyAt thermal equilibrium, hole current =0Hole gradient creates build-inelectric field to counteract the hole diffusion tendencyEE143 – Ali JaveyB-+[p]holes tend to moveaway due to holeconcentration gradientEbuild-inB-acceptorsexperiencean additionaldrift forceEnhanced Diffusion for B-acceptor atoms Electric Field EnhancementEE143 – Ali JaveyAsdiffusionUniform B conc in substratecaused by Asconc gradientB-Electric Field Enhancement – Substrate
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