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EE141 1© Digital Integrated Circuits2nd Wires
Digital Integrated Digital Integrated CircuitsCircuitsA Design PerspectiveA Design Perspective
The WireThe Wire
Jan M. RabaeyAnantha ChandrakasanBorivoje Nikolic
July 30, 2002
EE141 2© Digital Integrated Circuits2nd Wires
The WireThe Wire
transmitters receivers
schematics physical
EE141 3© Digital Integrated Circuits2nd Wires
Interconnect Impact on ChipInterconnect Impact on Chip
EE141 4© Digital Integrated Circuits2nd Wires
Wire ModelsWire Models
All-inclusive model Capacitance-only
EE141 5© Digital Integrated Circuits2nd Wires
Impact of Interconnect ParasiticsImpact of Interconnect Parasitics
Interconnect parasitics reduce reliability affect performance and power
consumption Classes of parasitics
Capacitive Resistive Inductive
EE141 6© Digital Integrated Circuits2nd Wires
10 100 1,000 10,000 100,000
Length (u)
No
of
net
s(L
og
Sc
ale)
Pentium Pro (R)
Pentium(R) II
Pentium (MMX)
Pentium (R)
Pentium (R) II
Nature of InterconnectNature of Interconnect
Local Interconnect
Global Interconnect
SLocal = STechnology
SGlobal = SDie
So
urc
e:
Inte
l
EE141 7© Digital Integrated Circuits2nd Wires
INTERCONNECTINTERCONNECT
EE141 8© Digital Integrated Circuits2nd Wires
Capacitance of Wire InterconnectCapacitance of Wire Interconnect
VDD VDD
VinVout
M1
M2
M3
M4Cdb2
Cdb1
Cgd12
Cw
Cg4
Cg3
Vout2
Fanout
Interconnect
VoutVin
CL
SimplifiedModel
EE141 9© Digital Integrated Circuits2nd Wires
Capacitance: The Parallel Plate ModelCapacitance: The Parallel Plate Model
Dielectric
Substrate
L
W
H
tdi
Electrical-field lines
Current flow
WLt
cdi
diint
ε=LL
Cwire SSS
SS
1=⋅
=
EE141 10© Digital Integrated Circuits2nd Wires
PermittivityPermittivity
EE141 11© Digital Integrated Circuits2nd Wires
Fringing CapacitanceFringing Capacitance
W - H/2H
+
(a)
(b)
EE141 12© Digital Integrated Circuits2nd Wires
Fringing versus Parallel PlateFringing versus Parallel Plate
(from [Bakoglu89])
EE141 13© Digital Integrated Circuits2nd Wires
Interwire CapacitanceInterwire Capacitance
fringing parallel
EE141 14© Digital Integrated Circuits2nd Wires
Impact of Interwire CapacitanceImpact of Interwire Capacitance
(from [Bakoglu89])
EE141 15© Digital Integrated Circuits2nd Wires
Wiring Capacitances (0.25 Wiring Capacitances (0.25 µµ m CMOS)m CMOS)
EE141 16© Digital Integrated Circuits2nd Wires
INTERCONNECTINTERCONNECT
EE141 17© Digital Integrated Circuits2nd Wires
Wire Resistance Wire Resistance
W
L
H
R = ρH W
L
Sheet ResistanceRo
R1 R2
EE141 18© Digital Integrated Circuits2nd Wires
Interconnect Resistance Interconnect Resistance
EE141 19© Digital Integrated Circuits2nd Wires
Dealing with ResistanceDealing with Resistance
Selective Technology Scaling Use Better Interconnect Materials
reduce average wire-length e.g. copper, silicides
More Interconnect Layers reduce average wire-length
EE141 20© Digital Integrated Circuits2nd Wires
Polycide Gate MOSFETPolycide Gate MOSFET
n+n+
SiO2
PolySilicon
Silicide
p
Silicides: WSi 2, TiSi 2, PtSi 2 and TaSi
Conductivity: 8-10 times better than Poly
EE141 21© Digital Integrated Circuits2nd Wires
Sheet ResistanceSheet Resistance
EE141 22© Digital Integrated Circuits2nd Wires
Modern InterconnectModern Interconnect
EE141 23© Digital Integrated Circuits2nd Wires
Example: Intel 0.25 micron ProcessExample: Intel 0.25 micron Process
5 metal layersTi/Al - Cu/Ti/TiNPolysilicon dielectric
EE141 24© Digital Integrated Circuits2nd Wires
INTERCONNECTINTERCONNECT
EE141 25© Digital Integrated Circuits2nd Wires
InterconnectInterconnectModelingModeling
EE141 26© Digital Integrated Circuits2nd Wires
The Lumped ModelThe Lumped Model
Vout
Driver
cwire
V i nC l u m p e d
R d r i v e rV o u t
EE141 27© Digital Integrated Circuits2nd Wires
The Lumped RC-ModelThe Lumped RC-ModelThe Elmore DelayThe Elmore Delay
EE141 28© Digital Integrated Circuits2nd Wires
The Ellmore DelayThe Ellmore DelayRC ChainRC Chain
EE141 29© Digital Integrated Circuits2nd Wires
Wire ModelWire Model
Assume: Wire modeled by N equal-length segments
For large values of N:
EE141 30© Digital Integrated Circuits2nd Wires
The Distributed RC-lineThe Distributed RC-line
EE141 31© Digital Integrated Circuits2nd Wires
Step-response of RC wire as a Step-response of RC wire as a function of time and spacefunction of time and space
0 0 .5 1 1 .5 2 2 .5 3 3 .5 4 4 .5 50
0 .5
1
1 .5
2
2 .5
tim e (n se c)
volta
ge (V
)
x = L /1 0
x = L /4
x = L /2
x= L
EE141 32© Digital Integrated Circuits2nd Wires
RC-ModelsRC-Models
EE141 33© Digital Integrated Circuits2nd Wires
Driving an RC-lineDriving an RC-line
V i n
R s V o u t
(rw,cw,L)
EE141 34© Digital Integrated Circuits2nd Wires
Design Rules of ThumbDesign Rules of Thumb
rc delays should only be considered when tpRC >> tpgate of the driving gate
Lcrit >> √ tpgate/0.38rc rc delays should only be considered when the
rise (fall) time at the line input is smaller than RC, the rise (fall) time of the line
trise < RC when not met, the change in the signal is slower
than the propagation delay of the wire
© MJIrwin, PSU, 2000
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