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Basic Interconnects. VLSI Design EE213. These slides contain some notes on interconnections in VLSI circuits. Full details are in Pucknell and Eshraghian pages 94 - 107. Introduction. Wiring-Up of chip devices takes place through various conductors produced during processing

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basic interconnects

Basic Interconnects

VLSI Design EE213

These slides contain some notes on interconnections

in VLSI circuits. Full details are in Pucknell and

Eshraghian pages 94 - 107

introduction
Introduction
  • Wiring-Up of chip devices takes place through various conductors produced during processing
  • Today, interconnects constitute the main source of delay in MOS circuits
  • We will examine:
    • Sheet Resistance – Resistance / Unit Area
    • Area Capacitance
    • Delay Units
    • CMOS Inverter Delay
    • Rise and Fall Time Estimation
sheet resistance
Sheet Resistance

A

  • Resistance of a square slab of material
  • RAB = ρL/A
  • => R = ρL/t*W
  • Let L = W (square slab)
  • => RAB = ρ/t = Rs ohm / square

t

w

L

B

RAB = ZRsh

Z = L/W

slide4

Typical sheet resistance values for materials

are very well characterised

Typical Sheet Resistances for 5µm Technology

slide5

N-type Minimum Feature Device

Polysilicon

L

N - diffusion

W

R = 1sq x Rs = Rs = 104Ώ

slide6

Polysilicon

W = 8λ

L = 2λ

N - diffusion

R = Z Rs

R = (L/W) * Rs

R = 4 104Ώ

slide7

Exercise

Calculate the ON resistance for a depletion pull – up

Nmos inverter with Zpu : Zpd ratio 4:1

Use sheet resistance values given in earlier slide

area capacitance of layers
Area Capacitance of Layers
  • Conducting layers are separated from each other by insulators (typically SiO2)
  • This may constitute a parallel plate capacitor, C = є0єox A / D (farads)
  • D = thickness of oxide, A = area,
  • єox = 4 F/µm2
  • Area capacitance given in pF/µm2
capacitance
Capacitance
  • Standard unit for a technology node is the gate - channel capacitance of the minimum sized transistor (2λ x 2λ), given as Cg
  • This is a ‘technology specific’ value
references
References
  • Pucknell and Eshraghian pages 94 - 102
delay unit
Delay Unit
  • For a feature size square gate, τ = Rs x Cg
  • i.e for 5µm technology, τ = 104 ohm/sq x 0.01pF = 0.1ns
  • Because of effects of parasitics which we have not considered in our model, delay is typically of the order of 0.2 - 0.3 ns
  • Note that τ is very similar to channel transit time τsd
cmos inverter delay
CMOS Inverter Delay
  • Pull-down delay = Rpd x 2 Cg
  • Pull-up delay = Rpu x 2Cg
  • Asymmetry in rise and fall due to resistance difference between pull-up and pull-down (factor of 2.5) (due to mobilities of carriers)
  • Delay through a pair of inverters is 2 τ (fall time) + 5 τ (rise time)
  • Delay through a pair of CMOS inverters is therefore 7 τ
cmos inverter delay13
CMOS Inverter Delay
  • Asymmetry can be improved by reducing resistance of pull - up
  • Reduce resistance of pull - up by increasing channel width ( typically by a factor of 2.5)
  • Note that increasing channel width also increases the capacitance
  • The overall delay (after increasing channel width by 2.5) will be the same 7 τ
cmos inverter rise and fall time estimation
CMOS Inverter Rise and Fall Time Estimation
  • Tf ~ 3CL / βVDD
  • Τr ~ 3CL / βVDD
  • (Derivations for the above are in Pucknell and Eshraghian Pages 105 - 107)
  • So, τ r/ τf = βn/βp
  • Given that (due to mobilities) βn = 2.5 βp, rise time is slower by a factor of 2.5 when using minimum dimensions of n and p transistors