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Berkeley ELENG 143 - Section 4 - Diffusion - part 2

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Section 4: Diffusion part 2Example : High Concentration Arsenic diffusion profile becomes “box-like”Summary of High-Concentration DiffusionTransient Enhanced Diffusion (TED)Diffusion: p-n Junction FormationSheet ResistanceResistivity vs. DopingIrvin’s CurvesMotivation to generate the Irvin’s CurvesResistivity Measurement: Four-Point ProbeImpurity Profiling: Spreading ResistanceImpurity Profiling Secondary Ion Mass Spectroscopy (SIMS)EE143 – Ali JaveySection 4: Diffusion part 2Jaeger Chapter 4EE143 – Ali JaveyExample : High Concentration Arsenic diffusion profile becomes “box-like”EE143 – Ali JaveyIf doping conc < ni :Use constant diffusivity solutions(profile is erfc or half-gaussian)If doping conc > ni :Solution requires numerical techniquesSummary of High-Concentration DiffusionEE143 – Ali JaveyTransient Enhanced Diffusion (TED)Dopant ImplantationSisubstrateImplantationinduced excesspoint defectsxC(x)no annealing900oC, several sec (TED)Extremely rapid diffusion due to excess point defectsImplantation createslarge number of excess Siinterstitials and vacancies.(1000X than thermal process).After several seconds of annealing, the excess point defects recombine.900oC, several minutes(After excess point defects recombine. slower diffusion)EE143 – Ali JaveyDiffusion: p-n Junction Formation⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛==B01-B0NNerfc 2 :profileFunction Error NNln 2 :ProfileGaussian doping) type-nout cancels doping type-p e. (i. zero ision concentrat impuritynet the wherepoint at the occursjunction n -PDepthJunction calMetallurgiDtxDtxxxjjjjEE143 – Ali JaveySheet ResistanceMaterial of Squares ofNumber Square]per [Ohms ResistanceSheet ==⎟⎠⎞⎜⎝⎛=⎟⎠⎞⎜⎝⎛=⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛=•=WLtRWLRWLtRtWASSρρEE143 – Ali JaveyResistivity vs. Dopingρ=σ−1= qμnn +μpp()[]−1n − type : ρ≅ qμnND− NA()[]−1p − type : ρ≅ qμpNA− ND()[]−1EE143 – Ali JaveyExplicitNo(surface concentration) ,xj(junction depth),NBRS(sheet resistance),p-type erfc n-type erfcp-type half-gaussiann-type half-gaussianIrvin’s Curvesrelationship between:(background concentration),EE143 – Ali JaveyApproach1) The dopant profile can be uniquely determined if one knows the concentration values at two depth positions.2) We will use the concentration values No at x=0 and NB at x=xj to determine the profile C(x). (i.e., we can determine the Dt value)3) Once the profile C(x) is known, the sheet resistance RS can be integrated numerically from:4) Irvin’s Curves are plots of No versus ( Rs• xj ) for various NB .()∫⋅=jxdxxNxqRs0)(1μAllows us to calculate doping parameters if we know 3 out of 4 of the parameters on the previous page Motivation to generate the Irvin’s CurvesEE143 – Ali JaveyResistivity Measurement: Four-Point ProbetMeasuremen ResistanceTerminalFour /square][ 53.42lnt>> sfor m]-[ 2lns>>for t m]-[ 2Ω≅==Ω=Ω=IVIVtRIVtIVsSπρπρπρEE143 – Ali JaveyImpurity Profiling: Spreading Resistance• Region of Interest is Angle- Lapped• Two-Point Probe Resistance Measurements vs. Depth• Profile ExtractedEE143 – Ali JaveyImpurity Profiling Secondary Ion Mass Spectroscopy


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Berkeley ELENG 143 - Section 4 - Diffusion - part 2

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