Wire Models Wires Professor Chris Kim University of Minnesota - - PowerPoint PPT Presentation

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Feb 27, 2023 270 likes •368 views

Wire Models Wires Professor Chris Kim University of Minnesota Dept. of ECE chriskim@umn.edu Capacitance-only All-inclusive model www.umn.edu/~chriskim/ 2 INTERCONNECT Capacitance of Wire Interconnect V DD V DD M 2 M 4 C db 2 C g 4 C gd 12

SLIDE 1

1

Wires

Professor Chris Kim

University of Minnesota

Dept. of ECE

chriskim@umn.edu www.umn.edu/~chriskim/

Wire Models

All-inclusive model Capacitance-only

INTERCONNECT

Capacitance of Wire Interconnect

VDD VDD Vin Vout M1 M2 M3 M4 Cdb2 Cdb1 Cgd12 Cw Cg4 Cg3 Vout2 Fanout Interconnect Vout Vin CL Simplified Model

SLIDE 2

2

Capacitance: The Parallel Plate Model

Dielectric Substrate L W H tdi Electrical-field lines Current flow

WL t c

di di int

ε =

L L Cwire

S S S S S 1 = ⋅ =

Permittivity

Fringing Capacitance

W - H/2 H

(a) (b) 8

Fringing versus Parallel Plate

(from [Bakoglu89])

SLIDE 3

3

Interwire Capacitance

fringing parallel

Impact of Interwire Capacitance

(from [Bakoglu89])

Wiring Capacitances (0.25 μm CMOS)

INTERCONNECT

SLIDE 4

4

Wire Resistance

W L H

R = ρ H W L Sheet Resistance Ro R1 R2

Interconnect Resistance

Dealing with Resistance

Selective Technology Scaling
Use Better Interconnect Materials

– reduce average wire-length – e.g. copper, silicides

More Interconnect Layers

– reduce average wire-length

Polycide Gate MOSFET

n+ n+ SiO2 PolySilicon Silicide p

Silicides: WSi 2, TiSi2, PtSi2 and TaSi Conductivity: 8-10 times better than Poly

SLIDE 5

5

Sheet Resistance

Modern Interconnect

Example: Intel 0.25 micron Process

5 metal layers Ti/Al - Cu/Ti/TiN Polysilicon dielectric

Modern Interconnect

90nm process

SLIDE 6

6

Interconnect Interconnect Modeling Modeling

The Lumped Model

Vout Driver cwire

lumped

driver

The Lumped RC-Model The Elmore Delay

The Elmore Delay: RC Chain

SLIDE 7

7

Wire Model

Assume: Wire modeled by N equal-length segments For large values of N:

The Distributed RC-line

Step-response of RC wire as a function of time and space

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 1.5 2 2.5 time (nsec) voltage (V) x= L/10 x = L/4 x = L/2 x= L

RC-Models

SLIDE 8

8

Driving an RC-line

(rw,cw,L)