Section 7: DiffusionDopant Diffusion SourcesFick’s First Law of DiffusionFick’s Second Law of DiffusionDiffusion Coefficients of Impurities in SiDiffusion CoefficientsDiffusion Mechanisms in Si Diffusion Mechanisms in Si Constant Source Diffusion Complementary Error Function ProfilesLimited Source Diffusion Gaussian ProfilesTwo Step Dopant Diffusion Normalized Concentration versus depthDiffusion of Gaussian Implantation ProfileSuccessive Diffusions: Thermal BudgetSolid Solubility LimitsHigh Concentration Diffusion EffectsElectric-field EnhancementElectric Field EnhancementElectric Field Enhancement – Substrate PerturbationEE143 – Ali JaveySection 7: DiffusionJaeger Chapter 4EE143 – Ali JaveyDopant Diffusion Sources(a) Gas Source: AsH3 , PH3 , B2 H6(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 10-6 cm2/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 Diffusion Complementary Error Function Profiles()()FunctionError ary Complement=erfctCoefficienDiffusion ionConcentrat Surface2, :Dose Total2, :ionConcentrat0000====⎟⎠⎞⎜⎝⎛=∫∞DNDtNdttxNQDtxerfcNtxNπEE143 – Ali JaveyLimited Source Diffusion Gaussian 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)()(ExampleDttotal of :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 important For 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 tends 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
View Full Document
Unlocking...