4_Pages from oxidation of silicon (Лекции Цветкова)

Oxidation of siliconCompetance goalsYou can:• Describe what oxides are used for• Describe different oxidation techniques• Describe the equipment• Explain the Deal-Grove model• Calculate oxide thicknes• Solve typical oxidation problems:•Analytically•Numerically using SupremeSilicon oxidationThe high quality of SiO2 is the reason for thesucces of silicon technology!Thermal oxide properties•Excellent dielectric:–Resistivity re >1016Wcm. Bandgap EG » 9eV–High breakdown field Ec » 1V/nm–Interface passivation.

Dit >109/eVcm2–Stable & reproducible bulk properties–Stable & reproducible Si/SiO2 interface–Perfect adhesion & low pinhole density < 1/cm2•Good masking properties–Low diffusivity for dopants–Easily etched selective to SiliconThanks to OHOxidation processSi → SiO2How would you do that?Dry oxidation :Si ( s ) + O2 ( g ) → SiO2 ( s )Wet oxidation :Si ( s ) + 2 H 2O( g ) → SiO2 ( s ) + 2 H 2 ( g )Oxidation technology• Thermally grown oxide• Wet• Dry• Deposited oxides• PECVD• LPCVD (e.g.

TEOS)• Electrochemical anodizationOxides are used for:• Gate oxide (dry)• Field oxide (wet)• Masking material• WaveguidesDryHigh∼1050°CWetHigh∼1000°CLPCVDMedium∼850°CPECVDLow∼300°CElectrochem.Very lowRoom tempOxidation FurnaceFlows: ∼5 slmPressure: ∼1 Bar = 105PaMIC - furnacesThermal oxidation in practice1.2.3.4.5.6.7.8.Clean the wafers (RCA)Put wafers in the boatLoad the wafers in the furnaceRamp up the furnace to process temperature in N2StabiliseProcess (Wet or Dry Oxidation)Anneal in N2Ramp downT1000OC20OC/min850OC2OC/mintimeSilicon consumptionThickness of Si used = 0.44 • Thickness of oxideStructure of silicon dioxideDensity 2.65g/cm3quartz crystal lattice – long range orderDensity 2.21g/cm3amorphous structure of silicon dioxide – short range orderDeal-Grove modelF1: Flux due to diffusionF2: Flux due to reactionProblem:How would you modeldiffusion and reaction?Deal Grove model: FluxF1: Diffusion – Ficks lawF2: Reaction – 1.st order reactionC0 − C sdCF1 = D=DdxxF2 = kCsSteady state :F1 = F2 = FDeal-Grove model: FluxC0 − C sF = kCsF=DxCombine and eliminate Cs :FC0 −C0 − C sDk=D⇒ xF = DC0 − FF=DkxxDDC0⇒  x +  F = DC0 ⇒F=kDx+ kDeal-Grove model: FluxDC0F=Dx+ kFor small x : F ≈ kC0Flux is limited by surface reaction!DC0For large x : F =xFlux is limited by diffusion!Deal-Grove model: Growth rateDC0F=Dx+ kFlux: Number of molecules persecond per cm2 {1/(cm2•s)}Growth rate: dx/dt {cm/s}O2Number of O2 molecules arriving:N = FAdtANumber of SiO2 created:N = C1dV = C1 AdxCombining :C0dx FD==FAdt = C1 Adx ⇒D  C1dt C1 x+ kdxSiO2dV = AdxN = C1dV = C1 AdxDeal-Grove model: Growth rateDC0 C0dx F==Growth rate =D  C1dt C1 x+ kIntegrate to find x(t )!Boundary conditions : x(0) = d 0Solution :2(22DCCkt +τ ) D2D200(t + τ ) x =  1 +− 1x +x=C1k DC1kThickness depends on square root of time!Deal-Grove model: Growth rateSolution :2(22Ckt +τ ) DC2DD200(t + τ ) x =  1 +− 1x=x +k DC1C1kFor small x ( x << 2 D / k ) :C0(t + τ ) the rate is dominated by surface reactionx≈kC1For large x ( x >> 2 D / k ):2 DC0(t + τ ) the rate is dominated by diffusionx2 ≈C1Deal-Grove model: In useConventional form :x + Ax = B(t + τ )22DA=k2 DC0B=C1 2 2 Dd 0 d0 +kτ =2DC 1 C011x = − A+A2 + 4 B (t + τ )22B(t + τ )ALarge x - parabolic region: x 2 = B(t + τ )Small x - linear region:x=The model is very good for wet oxidationFor dry oxidation a fitted value of τ must be used!Temperature and orientation dep.BSmall x - linear region:x = (t + τ )A2Large x - parabolic region: x = B(t + τ )Discuss:1) Should B/A depend on temperature?2) Should B/A depend on orientation of the substrate?3) Should B depend on temperature?4) Should B depend on orientation of the substrate?1+3) Yes – chemical reactions depend on exp(-Ea/kT)2) Yes – the surface reaction is important at small x3) No – at large x diffusion is rate limitingLinear rate constant B/A (um/h)T (C)Activation energy∼2eVBreak Si-Si bond:1.83 eV1000/T (K-1)Parabolic rate constant B (um2/h)T (oC)Wet:Ea=0.71eVDiffusion of water infused silica:Ea=0.79eVDry:Ea=1.24eVDiffusion of oxygen infused silica:Ea=1.18eV1000/T (K-1)Growth curves for dry oxidationGrowth curves for wet oxidationThin oxide growthWarning:Very thin (<20nm) dry oxides are not well described!There is a large compressive stress - lowers D ?Empirical model for dry oxidation:dxB−x=+ C expdt 2 x + A L L ≈ 7nmC/CBImpurity redistributionEquilibriu m concentration of impurity in siliconEquilibrium concentration of impurity in SiO2C/CBk=k<1k>1x (µm)x (µm)Oxide quality & thicknessThicknessmeasurement:a) Colorb) Profilerc) EllipsommetrySummaryThermal oxidation is the workhorse!Dry oxidation in oxygenWet oxidation in water vapourOxidation temperatures are around 1000CDeal-Grove model:x 2 + Ax = B(t + τ ) A =x=−2DkB=2 DC0C1 2 2 Dd 0 d0 +kτ =2D11A+A2 + 4 B (t + τ )22B(t + τ )A2Large x - parabolic region: x = B(t + τ )Small x - linear region:x=C 1 C0.