CS294-6Reconfigurable Computing

Day4

September 3, 1998

VLSI Scaling

Why Care?

• In this game, we must be able to predict the future

• Rapid technology advance

• Reason about changes and trends

• re-evaluate prior solutions given technology at time X.

Scaling

• Premise: features scale “uniformly”– everything gets better in a predictable manner

• Parameters: (lambda) -- Mead and Conway (class)– S -- Bohr– 1/ -- Dennard

Feature Size

Scaling

• Channel Length (L)• Channel Width (W)

• Oxide Thickness (Tox)

• Doping (Na)

• Voltage (V)

Scaling

• Channel Length (L) • Channel Width (W) • Oxide Thickness (Tox)

• Doping (Na) 1/• Voltage (V)

Effects?

• Area• Capacitance• Resistance

• Threshold (Vth)

• Current (Id)

• Gate Delay (gd)

• Wire Delay (wire)

• Power

Area

L * W

m m• 50% area• 2x capacity same area

Area Perspective

Capacitance

• Capacitance per unit area– Cox=SiO2

/Tox

– ToxTox/

– Cox Cox

Capacitance

• Gate Capacitance– Cgate= A*Cox

– Cox Cox

– Cgate Cgate /

Threshold Voltage

Threshold Voltage

• VTHVTH

Current

• Saturation Current– Id=(COX/2)(W/L)(Vgs-VTH)2

– Vgs=VV

– VTHVTH

– WW– Cox Cox

– IdId

Gate Delay

gd=Q/I=(CV)/I

• VV

• IdId

• C C /

gd gd /

Resistance

• R=L/(W*t)

• WW

• R R

Wire Delay

wire=RLC

• R R

• C C /

wire wire

• …assuming (logical) wire lengths remain constant...

Power Dissipation (Static)

• Resistive Power– P=V*I

– VV

– IdId

– PP

Power Dissipation (Dynamic)

• Capacitive (Dis)charging– P=(1/2)CV2f

– VV

– C C /

– PP

• Increase Frequency?– f f ?

– P P

Effects?

• Area 1/

• Capacitance 1/• Resistance • Threshold (Vth) 1/

• Current (Id) 1/

• Gate Delay (gd) 1/

• Wire Delay (wire) 1

• Power 1/1/

Delays?

• If delays in gates/switching?

• If delays in interconnect?

• Logical interconnect lengths?

Delays?

• If delays in gates/switching?– Delay reduce with 1/

Delays

• Logical capacities growing

• Wirelengths?– No locallity– Rent’s Rule

• L n(p-0.5)

• [p>0.5]

Capacity

• Rent: IO=C*Np

• p>0.5• AC*N2p

• Logical Area

AC*N22p

N2p N22p

N2 p) N

• Sanity Check– p=1

– N2 N

– p~0.5

– N2 N

Compute Density

>compute density scaling>

gates dominate, p<0.5moderate p, good fraction of gate delaylarge p (wires dominate area and delay)

Power Density

• PP (static, or increase frequency)

• PP(dynamic, same freq.)

• P/A P/A … or … P/A

Scaling Summary

• Uniform scaling reasonably accurate for past couple of decades

• Area increase

– Real capacity maybe a little less?

• Gate delay decreases (1/)

• Wire delay not decrease, maybe increase

• Overall delay decrease less than (1/)