Ch.5-Ch.7-2011

Ch.5-Ch.7-2011 - 2/1/2011 1 Layout and Matching Resistor...

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Unformatted text preview: 2/1/2011 1 Layout and Matching Resistor and Resistor Networks Ch.5 and Ch.7 1 Chap.5 Resistors-Introduction-Layout 2 1. Resistivity and Sheet Resistance r [ W-cm] = resistivity s [1/ W-cm] = 1/ r . Material Resistivity, r W-cm (at 25 o C) Copper, bulk 1.7E-6 Gold, bulk 2.4E-6 Al, thin film 2.7E-6 Al (2% Si) 3.8E-6 Pt silicide 3.0E-5 n-Si (Nd=1E18) 0.25 n-Si (Na=1E15) 48 i-Si 2.5E5 SiO 2 ~1E14 3 2/1/2011 2 R = r L / W t Define R s or r sh r / t R = R s L / W, where R s is in [ W / ] Uniform Bulk: Thin Layers: I I 4 2. Resistor Layout R = R s L d / (W d + W b ) W b = Width bias due to outdiffusion 20% of junction depth Example) If base resistor junction depth = 1.25 um, then W b 0.25 um W d = 5um W d + W b 5.25 um (5% error) W d =20um W d +W b =20.25um (1.25% error) L d = drawn length W d = drawn width W b = width bias 5 Effect of lateral nonuniform current flow Current Crowding correction due to current crowding inward near contacts: k = W e / (W e-W c ): W e = W d + W b = effective width , W c = contact width ex) Suppose W e = 5um, W c = 3um => D R/R s = 0.0523 0.05 squares longer Most resistors = at least 10 s long => D R/R < 1% error Contact resistance = Current in resistor must flow upward and vertically, crowding inward at the metal contacts. W c 6 2/1/2011 3 Comment: W b is usually important . Nonuniform flow is usually not important. Ex) If R = at least 5 squares long nonuniform (lateral or vertical) current flow < 5% error 7 ii) Large resistors: serpentine or folded Each square corner = 0.56 s R = R s [ (2A+B)/W + 1.12] Each round (180 degrees) segment = 2.96 squares . R = R s ( 2C/W + 2.96) 8 needs a wider contact area than the resistor body Dog-bone or dumbbell shape Current spreads out as it enters contact: make W c = W d to reduce effect Minimize W o (overlap width) the correction factor: usually 0.3 Very narrow resistors 9 2/1/2011 4 Relative Packing . notice the location of contact head 10 3. Resistor Variability (1) Process Variation R = R S *L/W D R S =due to film thickness fluctuation, doping density and profile fluctuation, and anneal condition; D W, D L = innacuracies in lithography and etch rate non-uniformity. Modern processes: D R S within 20% or 25% (but base-pinch R is similar to b variation, 50%). D L toloerance of 1um is same whether L=5um or L=25um . So, larger size has better accuracy. Most processes can maintain 20% of min. size. Let C L =linewidth control of the layer, d R=R-tolerance, and d R S =R S-variation, then Actual of R : d R = C L /W e + d R S Ex) If C L = 0.25um, d R S = 25%, then W e =2um : d R = C L /W e + d R S = 0.25/2 + 25% = 12.5% + 25% = 38% W e =10um : d R = 0.25um/10um + 25% = 28% 11 Summary: For d R S = 25% and C L = 20% min.size, 1. Where tolerance does not matter , use minimum-width resistors and expect variations of about 50% . Diffused resistors should not be made narrower than about 150% of their junction depth, or the amount of dopant may be inadequate...
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Ch.5-Ch.7-2011 - 2/1/2011 1 Layout and Matching Resistor...

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