Chap'5 Resistors

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Chap.5 Resistors

• Introduction
• Layout

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• Resistivity and Sheet Resistance
• r W-cm resistivity s 1/W-cm 1/ r.
• Material Resistivity, W-cm (25C)
• 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 (Nd1E18) 0.25
• n-Si (Na1E15) 48
• i-Si 2.5E5
• SiO2 1E14

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Uniform Bulk
R r L / W t
Thin Layers
Define Rs r / t ? R Rs L / W,
where Rs is in W/square
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2. Resistor Layout R Rs Ld / (Wd
Wb) Wb bias due to outdiffusion about
20 of junction depth Ex) If base resistor
junction depth 1.25 um, then Wb 0.25
um Wd 5um ? Wd Wb 5.25 um (5 error)
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Effect of lateral nonuniform current flow due to
current crowding inward near contacts DR (Rs
/ p) (1/k) ln((k1)/(k-1)) ln ((k2-1)/k2)
k We / (We-Wc) We Wd Wb effective
width, Wc contact width ex) Suppose We
5um, Wc 3um gt DR/Rs 0.0523 0.05
squares longer Most resistors at least 10
squares long gt DR/R lt 1 error Contact
resistance Current in resistor must flow
upward, vertically, and crowd inward at the
metal contacts.
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Comment Wb is usually important.
Nonuniform flow is usually not
important. Ex) If R at least 5 squares long ?
nonuniform (lateral or vertical) current flow
lt 5 error
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ii) Large resistors serpentine or folded Each
square corner 0.56 squares R Rs
(2AB)/W 1.12
Each round (180 degrees) segment 2.96
squares. R Rs ( 2C/W 2.96)
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Very narrow resistors

• needs a wider contact area than the resistor
  body
• Dog-bone or dumbbell shape
• Current spreads out as it enters contact
  make Wc Wd to reduce effect
• Minimize Wo (overlap width)
• the correction factor usually 0.3 squares

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Relative Packing .