1Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Thermal Oxidation of Si• General Properties of SiO2• Applications of thermal SiO2• Deal-Grove Model of OxidationThermal SiO2is amorphous.Weight Density = 2.20 gm/cm3Molecular Density = 2.3E22 molecules/cm3Crystalline SiO2[Quartz] = 2.65 gm/cm3SiO2<Si>2Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Thermal SiO2Properties(1) Excellent Electrical InsulatorResistivity > 1E20 ohm-cmEnergy Gap ~ 9 eV(2) High Breakdown Electric Field > 10MV/cm(3) Stable and Reproducible Si/SiO2Interface(4) Conformal oxide growth on exposed Si surfaceSiSiSiO2ThermalOxidationSiSiSiSiO2ThermalOxidation3Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05(5) SiO2is a good diffusion mask for common dopantsDDsio si2<<e.g. B, P, As, Sb. (6) Very good etching selectivity between Si and SiO2.SiO2SiSiO2SiHF dip*exceptions are Ga(a p-type dopant) and some metals, e.g. Cu, Au*exceptions are Ga(a p-type dopant) and some metals, e.g. Cu, AuThermal SiO2Properties – cont.Si4Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Steam generationfor wet oxidation5Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Thickness of Si consumed during oxidationsioxoxsiNNXX •=oxoxXcmatomscmmoleculesX 46.0/105/103.2322322=××=•XsiSiSiSiO2originalsurfaceXoxmolecular density of SiO2atomic density of Si6Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F051µm Si oxidized2.17 µm SiO2For 1-dimensional planar oxide growthSuggested calculation exercise:Si1 µm diameterSi sphereSiO21.3 µm diameterSiO2 spherecompletelyoxidized7Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Kinetics of SiO2GrowthGas DiffusionSolid-stateDiffusionSiO2FormationSi-SubstrateSiO2Oxidant Flow(O2or H2O)Gas FlowStagnant Layer8Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Deal-Grove ModelCGCsCoCiX0xstagnantlayerSiO2SiF1F2F3gastransportfluxdiffusionfluxthrough SiO2reactionfluxat interfaceNoteCs≠ CoNoteCs≠ Co9Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05()FhC CGG S1=−xCDF∂∂−=2−⋅≅oxioXCCDisCkF ⋅=3Diffusivity [cm2/sec]Mass transfer coefficient [cm/sec].“Fick’s Law of Solid-state Diffusion”Surface reaction rate constant [cm/sec]Comment: The derivation used in Jaeger textbook assumes F1 is large (not a rate-limiting factor for growth rate).Hence, the algebra looks simpler. However, the lecture notes derivation includes gas transport effect and can be directly applied to CVD growth rate which will be discussed in later weeks.10Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05• CSand Coare related by Henry’s Law• CGis a controlled process variable (proportional to the input oxidant gas pressure) Only Coand Ciare the 2 unknown variables which can be solved from the steady-state condition: F1= F2=F3 ( 2 equations) Only Coand Ciare the 2 unknown variables which can be solved from the steady-state condition: F1= F2=F3 ( 2 equations) How to solve the oxidant concentrations?11Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05soPHC⋅=()sCkTH⋅⋅=partial pressure of oxidantat surface [in gaseous form].Henry’sconstantfrom ideal gas law PV= NkTHkTCCos=∴Derivation of Oxidation Growth RateHenry’s Law12Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05)(GACHkTC⋅≡FhHkTCCGAo1=−( )321FFF==DefineUsing the steady-state condition:2 equations to solve the2 unknowns: Co& Ci2 equations to solve the2 unknowns: Co& Ci1 2h≡This is a controlprocess variable.For a given oxidantpressure, CAis known. F1can be re-written as:Derivation of Oxidation Growth Rate – cont.Conservation of mass flux13Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05CCkhkXDiAssox=++1+⋅=DXkCCoxsio1()DXkhkCkCkFFFFoxssAsis++=⋅====1321ThereforeDerivation of Oxidation Growth Rate – cont.14Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Now, convert F into Oxide Thickness Growth Rate ⋅=dtdXNFox1Oxidant molecules/unit volume required to form a unit volume of SiO2.SiO2SiF∆Xox{}∆tTherefore, we have the oxide growth rate eqn:++=•DXkhkCkdtdXNoxssAsox1115Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F0512)11(2NDCBhkDAAs≡+≡BAXXii+=2τInitial Condition: At t = 0 , Xox= Xi)(2τ+=+tBAXXoxoxSolutionNote: h >>ksfor typical oxidation conditionSiO2SiSiO2Sixox16Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Note : “dry” and “wet” oxidation have different N1factorsNcm122 323 10=×./for O2as oxidantSi O SiO+→22Si H O SiO H+→+↑22222Ncm122 346 10=×./for H2O as oxidant17Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05BdtdxAdtdxXtBAXXoxoxoxxox=++=+2)(02τSummary of Deal-Grove Model∝t∝tXoxtoxoxXABdtdx2+=∴Oxide Growth Rate slowsdown with increase of oxide thicknessOxide Growth Rate slowsdown with increase of oxide thickness18Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05XAtABox=++−21412τ(Case 1) Large t [ large Xox]BtXox→(Case 2) Small t [ Small Xox]tABXox→19Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Deal-Grove Model ParametersDNCDBA∝≡12kTQeD−∝(1)(2)1AsNC)k1h1(1AB+=Q = activation energyfor diffusionFor thermal oxidation of Si, h is typically >> ksB/A is ∝ks(i.e. F1is rarely the rate-limiting step)For thermal oxidation of Si, h is typically >> ksB/A is ∝ks(i.e. F1is rarely the rate-limiting step)kTQs'ek−∝Q’ = activation energyfor interface reaction20Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05B = Parabolic ConstantB/A = Linear Constant21Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Oxidation ChartsThe charts arebased on Xi = 0 !The charts arebased on Xi = 0 !22Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Two Ways to Calculate Oxide ThicknessGrown by Thermal OxidationE.g.SiO2Si4000Axi=1100oC33minsteamSiO2SixoxMethod 1: Find B & B/A from ChartsSolve )(2τ+=+tBAXXoxox23Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05Method 2: Use Oxidation ChartsThe charts arebased on Xi =0 !The charts arebased on Xi =0 !min244000=⇒=τAXiat 1100oC from chartTotal effective oxidation timemin57min)3324(=+if start with 0=iX∴XoxT3T2T11100oC6500oA4000oA24 3357time(min)0Two Ways to Calculate Oxide ThicknessGrown by Thermal Oxidation24Professor N. Cheung, U.C. BerkeleyLecture 5EE143 F05SiO2Si4000oASiO2Si4000oASiO2Si4000oAxiCVDOxide(1) Grown at 1000oC, 5hrs(2) Grown at 1100oC, 24min(3) CVD OxideFor same Xi, τ is the same
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