Technology Trends in Power-Grid-Induced Noisesliponline.org/SLIP02/session2/nassif.pdf · 3 Motivation Power is increasing (hot plates, nuclear reactors etc…). V DD is decreasing

Technology Trends in Power-Grid-Induced Noise

Onsi [email protected]

Sani R. NassifIBM Research – [email protected]

2

ITRS Power Fashion Statement

0

20

40

60

80

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140

160

180

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1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Years

nano

-met

ers

Technology Node DRAM 1/2 Pitch MPU Gate Length ASIC Gate Length

0

20

40

60

80

100

120

140

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180

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1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Years

Max

Pow

er D

issi

patio

n (W

)

1

1.5

2

2.5

3

3.5

4

Max

Pow

er D

issi

patio

n (W

)

Desktop Portable

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Years

Supp

ly V

olta

ge (V

)

High Performance Low Power

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1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Y ear s

Sup

ply

Cur

ren

t (A

)

0

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4

6

8

10

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Sup

ply

Cu

rren

t (A

)

Des ktop , h igh pe r fo r mance Por tab le , low pow er

Farid Najm (from *TRS data)

3

MotivationPower is increasing (hot plates, nuclear reactors etc…).

VDD is decreasing (VTH decreasing slower to manage leakage).

Frequency is increasing.Dynamic and static IDD are increasing (electromigration!).

IR and Ldi/dt noise becoming a larger part of the total noise budget.Impact of VDD variation on delay is increasing.

(Because of reduced overdrive VDD-VTH)

Understanding the origins and trends of supply induced noise becoming critical.

4

Leakage Current “Predictions”

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1990 1995 2000 2005 2010 2015 2020

NTRS '97ITRS '99ITRS '01

I OFF

@ 2

5°C

(nA/

µm)

Tak Ning (from *TRS data)

5

OutlineExpressions for power grid induced noise.Technology trends.

Design realities and trends…Power Grid Planning.Power Grid Planning Examples.

Open issues and low-hanging fruit.

6

Canonical Power Grid CircuitGrid is predominantly resistive.Package is predominantly inductive.Load is current.Other circuits ~ lossy decoupling capacitance.

VDD

+

LoadDecouplingCapacitance

GridPackageCurrent

time

7

Grid CapacitanceCapacitance ~ 1/distance.

Distance scale for power grid is in the range of 10µm.

Distance scale for device capacitance is in the range of TOX ~ 20nm.

Capacitance “density” of devices makes grid capacitance unimportant.

8

Grid InductanceRectangular Conductor…Worst case for grid wire.L(pH) ~ 0.2 l ln(2l/(w+t) + 0.5)Package parasitics much greater.

w

l

t

10

100

1000

10000

100 1000 10000

Length (microns)

Indu

ctan

ce (p

H)

Range of Package

9

Grid Resistance

0.1

1

10

100

100 1000 10000

Length (microns)

Res

ista

nce

(ohm

s)

Same Conductor…R ~ 0.1 l/(w t)Package parasitics much smaller.

w

l

t

Range of Package

10

Noise ModelCurrent modeled as:I = 0 t < 0I = µt t < tpI = µ(2tp-t) t < 2 tp

I = 0 t > 2 tp

Ignoring L, maximum noise is:Vmax= µ tp Rg – µ R2

g Cd (1 – e-tp/τ)

τ = (Rg + Rd) Cd

VDD

+Rg

Rd

Cd

DC Decap

l µ tp Rg / (Rg + Rd)(for large Cd)

Current

timetp

µ

L

11

VDD

+Rg

Rd

Cd

LNoise Model + L

With package, maximum noise becomes:Vmax l µ tp Rg + µL – µ R2

g Cd (1 – e-tp/τ)

Accurate expression:Vmax = µ tp Rg + µL – µ R2

g Cd + ψ1 + ψ2

e1 = exp –(τ+β)tp/2CdL e2 = exp –(τ–β)tp/2CdLβ = (τ2 – 4LCd)½

ψ1 = (e1 + e2) µ (L – Cd Rg

2) / 2ψ

2 = (e1 – e2) µ Cd (τ Rg2 – L(3Rg-Rd)) / 2β

DC DecapPackage

12

Quality of Approximation

1.00E-04

1.00E-03

1.00E-02

1.00E-04 1.00E-03 1.00E-02

Accurate Formula

Appr

oxim

ate

Form

ula

Overestimation

~2X

Good accuracywhere needed!

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14

Technology VariablesWe need to find trends in the parameters of our canonical model.Roadmaps provide insight into VDD, Area, Power, Frequency etc…

VDD

+Rg

Rd

Cd

L

Current

timetp

µ

15

Technology Parameters

0.261606221.220006520050.251505951.218577020040.251405671.517248020030.261305091.516008520020.261154501.5145410020010.221004501.8132112020000.2904501.812001401999

Power Density

Power(Watts)

Area(2mm)

VDD(Volts)

F(MHz)

LEFF(nm)

Year

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DependenciesTime tp ~ F-1

Power density P ~ VDD µ tp → µ ~ F P / VDD

Cd ~ COX ~ 1/TOX

Rd and Rg are ~ constantBut proper power grid planning can make a difference here!

L is ~ constantPackage learning curve is much shallower than technology learning curve!

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VDD

+Rg

Rd

Cd

LNoise TrendsVDD

tpµ

Cd

0.6X

0.6X

3.3X

2X

Based on conservative ITRS trends

~2X ~3X

Vmax l µ tp Rg + µL – µ R2g Cd (1 – e-tp/τ)

DC DecapPackage

~Same

Plus ~ 1.7X due to reduction in VDD

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19

Power Grid Design TrendsNumber of levels of metal is increasing.

More degrees of freedom for tradeoff between interconnect and power.More effort in grid design.

Cu and advanced CMP processes place more design restrictions on wires.

Example: maximum width, metal density, oxide density within metal area, etc…

Number of package power pins for high power chips increasing (fixed Imax per pin).

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Package Choices

Area Array (C4)Power distributed across all the chip area.

Wirebond (periphery)Power brought in from edge of chip.

21

SOC and IP ConstraintsHard IP places constraints and creates discontinuities in grid design.Often dealt with using “rings” (area hit).

Ring

Hard IPBlock

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Power Grid Design IssuesPower Grid impacts implementation of every component at the PD level.Placement of power-hungry devices (I/O buffers, clocks, etc…).Placement and allocation of decoupling capacitors to minimize noise.“Interface” between incompatible power distributions costly in routing resources.

It is not unthinkable to use 15 to 20% of wiring resources for power distribution.

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Buffer Placement AlgorithmICECS ‘00 paper (J. Kozhaya et. al.)

A greedy heuristic technique.Idea: Use sensitivity information to place I/O buffers one at a time while satisfying drop thresholds.The A-1 (system matrix) provides sensitivity of voltage drops to placement of I/O buffers.

I/O buffers only appear in the RHS of the system of linear equations!

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Algorithm Description1. Sort I/O buffers and initialize drop slacks.2. For buffer Bk, compute upper bounds on the

allowable current at every node ni which is a potential placement site.

3. Assign buffer Bk to node nm where nm is the node with the largest upper bound.

4. Update the drop slack at all nodes:s(j) = s(j) – ajm

-1 Ik, ≤j

5. If s(j) < 0, report a violation at node nj.6. Continue at step 2 with the next buffer.

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Results

3.0403325588C2 (0.13µ)

3.7904602616C1 (0.18µ)

CPU TimeViolations# Nodes# BuffersDesign

Technique finds a feasible placement.CPU time is fast enough for iteration.Results were verified using detailed simulation.

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Is This an Easy Problem?Results of placing the I/Os randomly with 1.0% drop thresholds:

0 250 500 750 1000 1250 15000

50

100

150

200

250

300

Number of violations

Fre

quen

cy o

f num

ber

of v

iola

tions

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Decoupling Capacitance SizingUpcoming DAC’02 paper (H. Su et. al.)

After optimizationBefore optimization

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Impact of Decap Sizing

0.00

0.05

0.10

0.15

0.20

60% 65% 70% 75% 80%

Occupancy

Noi

se m

etric

before optimizationafter optimization

Decap optimization allows ~10% more circuit density!

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Power Grid PlanningPower grid is usually designed BEFOREdetailed implementation has started.

Predefined “Image” for ASIC or SOC implementations.“Tile” based image for custom ICs.

Grid is defined at a time when the spatial information about power requirements is approximate, therefore rampant overdesign!

31

IBM Power Grid Planner

Spreadsheet-like interface to define overall power grid.

32

IBM Power Grid PlannerLots of Visualization and Analysis…

33

IBM Power Grid PlannerUsually used to explore design options very early in the design cycle.Tool needs to be very fast (interactive).

Typical questions:Can a grid with X% density handle P watts per square mm?How much decoupling capacitance does an I/O buffer need? How close does it need to be?How much do I gain by introducing skew?

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35

Planning ExamplesQuestion:

What is the impact of wiring resources on a per layer basis?

Methodology:Perform a full factorial experiment varying wiring density on each level from 5% to 20% and measure grid performance.Build a statistical model of grid performance vs. layer densities.

36

Experiment7 level metal process.Top level fixed to interface to package C4’s.

Density ~ width/pitch.Pitch goes up by 2X every 2 layers (1,1,2,2,4,4)

46 = 4096 simulation ~ 10 hours CPU time.

Measure VDD and GND net statistics.

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Example of Results

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

9.00E-02

1.00E-01

1.10E-01

1.20E-01

0 0.05 0.1 0.15 0.2 0.25

Density on Layer 6

Mea

n V D

Ddr

op

38

Analysis of ResultsLinear regression of noise vs. layer densities.

name vddmax vddmean gndmax gndmeanrho 0.948 0.941 0.939 0.935range 0.0527,0.1804 0.0364,0.1142 0.0360,0.1296 0.0182,0.0585

K 0.18164 0.12115 0.12010 0.05549

d0 -0.02428 -0.00001 -0.02616 -0.00520d1 -0.10201 -0.03502 -0.13665 -0.06095d2 -0.02937 -0.00537 -0.02764 -0.00739d3 -0.12701 -0.06568 -0.13211 -0.06287d4 -0.05253 -0.03394 -0.02857 -0.00947d5 -0.39699 -0.33490 -0.13706 -0.06973

Directional dependence! (anisotropy)

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40

Open IssuesCoupling of power and timing results.

Some early results, but nothing real yet!

Fast modeling and prediction of chip/package resonance.

Approximations OK, but better numerical analysis can make results more accurate.

Vector-less Chip-level power estimation.Most design flows are not yet focused on power. Need a method to jumpstart power analysis.

Coupling of power and thermal results + impact on reliability.

Same math, same inputs…

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Low Hanging FruitImproved modeling of load currents and decoupling capacitance.

Holistic rationalization of accuracy requirements.

Integration of placement aspects of PD with power grid analysis.

Moving loads around can be done very efficiently (new RHS and forward/backward solver of existing LU factors).

Use of sparse inductance formulations to speed up chip/package analysis.

Reuse of existing simulation infrastructure.

Documents

Technology Trends in Power-Grid-Induced Noisesliponline.org/SLIP02/session2/nassif.pdf · 3 Motivation Power is increasing (hot plates, nuclear reactors etc…). V DD is decreasing