1

Interconnect and PackagingLecture 2: Scalability

Chung-Kuan ChengUC San Diego

2

Outlines

I. Trends of Interconnect and Packaging

II. Scalability

References

3

I. Trends of High Performance Interconnect and Packaging

Year 2011 2015 2020 2025

D1/2 Pitch, nm 40 25 14 7

#metal layers 12 13 14 -

Ave permittivity 2.99 2.78 2.23 1.99

M1 pitch, nm/AR 76/1.8 42/1.9 24/2.0 13/2.2

M1 cap, pF/cm 1.9-2.1 1.8-2 1.6-1.8 1.5-1.8

RC delay, ns/mm 3.429 15.164 56.834 224.749

Int pitch, nm/AR 76/1.8 42/1.9 24/2.0 13/2.2

Int cap, pF/cm 1.7-1.9 1.6-1.9 1.3-1.6 1.1-1.5

RC delay, ns/mm 3.168 13.741 48.203 192.495

Glob pitch, nm 354-190 482-190 702-190 1125-190

Glob cap, pF/cm 2.0-2.3 1.8-2.2 1.4-1.8 1.2-1.6

RC delay, ns/mm 0.999 4.012 14.814 67.913

4

I. Trends of High Performance Interconnect and Packaging

Year 2005 2010 2011 2015 2020 2024

D1/2 Pitch, nm

80 45 40 25 14 9

Chip size, mm2

310 310 140-750 140-750 140-750 140-750

Pin count 3,400 4,009 720-5094 880-6191 1050-7902 1212-9148

Cents/pin 1.78 1.37 0.57-1.48 0.46-1.21 0.35-0.94 0.30-0.77

On-chip (MHz)

5,170 12,000

6,330 8,520 12,360 15,410

Off-chip (MHz)

3,125 10,000

12,000 30,000 55,000 75,000

Power Density w/mm2

0.54 0.64 0.7-0.55 0.9-0.75 1.15-1 1.35-1.20

5

I. Trends

• On-Chip Interconnect

• Delay (5-40 times of Speed of Light 5ps/mm)

• Power Density (> ½)

• Clock Skew: Variations (5GHz)

• Off-Chip Interconnect and Packaging• Number of pins (limited growth)

• Wire density (scalability)

• Speed and distance of interconnect

6

I. Trends

• On-chip Global Interconnect trend

• Concerns: Speed, Power, Cost, Reliability

0

40

80

120

160

200

180 150 130 100 90 80 70 65 57 50Process Technology Node (nm)

Dela

y (p

s)

1mm Global I nterconnect with Scattering(source: I TRS Roadmap 2004)

FO4 I nverter Delay (Estimated by0.36*Ldraw)

1mm distortionless Transmission Line (Speedof Light)

7

I. Trend

• Scalability• Latency, Bandwidth• Attenuation, Phase Velocity

• Distortion• Intersymbol Interference, Jitter, Cross Talks

• Clock Distribution• Skew, Jitter, Power Consumption

• IO Interface• Density• Impedance Matching• Cross Talks, Return loops

8

II. Scalability: Interconnect Models

RΔl LΔlCΔl

RΔl LΔl

CΔl …

i(z,t)

RΔl LΔl RΔl LΔl

Voltage drops through serial resistance and inductance

Current reduces through shunt capacitance

Resistance increases due to skin effect

Shunt conductance is caused by loss tangent

9

II. Scalability: Interconnect Models• Telegrapher’s equation:

),(),(),(

),(),(

),(

tzGVdt

tzdVC

dz

tzdIdt

tzdILtzRI

dz

tzdV

• Propagation Constant:

jCjGLjR ))((

• Wave Propagation:

//,),( 0 tzveVtzV tjzjz

• Characteristic Impedance

)/()( CjGLjRZ

10

II. Scalability of Physical Dimensions• R= ρ/A = ρ/(wt)• Z= ¼ (µ/ε)1/2 ln (b+w)/(t+w)• C= vZ• L= Z/v

b

w

t

ρ: resistivity of the conductorµ: magnetic permeabilityε: dielectric permittivityv: speed of light in the medium

11

II. Scalability of Physical Dimensions • Resistance: Increases quadratically with

scaling, e.g. ρ=2µΩ-cm

R=0.0002 Ω/µm at A=10µmx10µm

R=0.02 Ω/µm at A=1µmx1µm

R=2 Ω/µm at A=0.1µmx0.1µm

• Characteristic Impedance: No change

• Capacitance per unit length: No change

• Inductance per unit length: No change

12

II. Scalability of Frequency Ranges

1. RC Region

2. LC Region

3. Skin Effect

4. Loss Tangent

13

II. Scalability of Frequency Ranges

2/2/

))((

RCjRCRCj

CjGLjRj

1. RC Region 0,/ GLR

RCv

jwC

RZ

2,

e.g. on-chip wires R=2ohm/um (A=0.01um2)L=0.3pH/um, C=0.2fF/umR/L=6.7x1012

14

II. Scalability of Frequency Ranges: RC Region

gw

w

wg

ns

sclcc

lrr

lcsfcc

srr

2/

2/

/

2

1

1

Elmore delay model with buffers inserted in intervals

ltr: length from transmitter to receiverl: interval between buffersrn: nmos resistancecn: nmos gate capacitancecg=(1+g)cn, g is pn ratio.rw: wire resistance/unit lengthcw: wire capacitance/unit lengthf: cd/cg

l

ltr

l

llscrl

crcfslc

s

rlDelay tr

gwww

gwn

tr }2

))1(({)( 2

15

II. Scalability of Frequency Ranges: RC Region

l

llscrl

crcfslc

s

rlDelay tr

gwww

gwn

tr }2

))1(({)( 2

ww

gn

cr

crfl

)1(2

gw

wn

cr

crs

Elmore delay model with buffers inserted in intervals

Optimal interval

wgwntrtr ccrrfllDelay ))1(22(/)(

Optimal buffer size

Optimal delay

16

II. Scalability of Frequency Ranges

mcr

crfl

ww

gn 242)1(2

41gw

wn

cr

crs

Example: w= 85nm, t= 145nm

Optimal interval

mmpsmfsccrrfllDelay wgwntrtr /194/194))1(22(/)(

Optimal buffer size

Optimal delay

rn= 10Kohm,cn=0.25fF,cg=2.34xcn=0.585fFrw=2ohm/um, cw=0.2fF/um

17

II. Scalability of Frequency Ranges: RC Region

Year

(On-Chip)

2005 2010 2015

rncn (ps) 0.86 0.39 0.18

rwcw (ps/mm)* 284 616 1510

l (um) 168 77 33

D (ps/mm) 96 95 101

*no scattering, p=2.2uohm-cm

18

II. Scalability of Frequency Ranges: RC Region

• Device delay, rncn, decreases with scaling

• Wire delay, rwcw, increases with scaling

• Interval, l, between buffers decreases with scaling

• In order to increase the interval, we add the stages of each buffer.

19

II. Scalability of Frequency Ranges2. LC Region 0,/ GLR

LCjZ

RCjLjR

CjGLjRj

2)(

))((

LCvCLZ /1,

20

II. Scalability

3. Skin Effect Skin Depth:

/2

)2/( ZR

21

II. Scalability

3. Skin Effect Skin Depth:

/2

)2/( ZR

e.g. 0.7um @ f=10GHz, ρ=2uΩ-cmFor 100umx25umRDC=0.000008Ω/um= 8Ω/mR= 0.000114Ω/um=114Ω/m

22

II. Scalability4. Loss Tangent

tan),tan1( 0,00 CGCCj

)(/62/,02.0tan polyimidemGZp

)(/6.02/,002.0tan glassmGZg )(/06.02/,0002.0tan quartzmGZq

LCjGZ

Z

R

CjGLjRj

22

))((

23

References• E. Lee, et al., “CMOS High-Speed I/Os – Present and Future,” ICCD

2003.• http://www.itrs.net/• Ling Zhang, Low Power High Performance Interconnect Design and

Optimization, Thesis, UCSD, 2008.• G.A. Sai-Halasz G.A. "Performance Trends in High-End Processors,“

IEEE Proceedings, pp. 20-36, Jan. 1995.• M.T. Bohr, “Interconnect scaling-the real limiter to high performance

ULSI” Electron Devices Meeting, 1995., International10-13 Dec. 1995 pp.241 – 244.