Defocus-Aware Leakage Defocus-Aware Leakage Estimation and ControlEstimation and Control

Andrew B. KahngAndrew B. Kahng†‡†‡

Swamy MudduSwamy Muddu‡‡

Puneet SharmaPuneet Sharma‡‡

CSECSE†† and ECE and ECE‡‡ Departments, UC San Departments, UC San DiegoDiego

OutlineOutline

► Systematic Components of Linewidth Systematic Components of Linewidth VariationVariation

► Defocus-Aware Leakage Estimation Defocus-Aware Leakage Estimation ► Experimental StudyExperimental Study► Defocus-Aware Leakage OptimizationDefocus-Aware Leakage Optimization► SummarySummary

Leakage PowerLeakage Power► Leakage power limits large, high-performance Leakage power limits large, high-performance

designs in sub-100nm regimedesigns in sub-100nm regime► Decreasing threshold voltages (VDecreasing threshold voltages (Vthth) boost ) boost

performance but increase leakageperformance but increase leakage► Components of leakage powerComponents of leakage power

Subthreshold leakageSubthreshold leakage Gate leakageGate leakage Band-to-band tunneling leakageBand-to-band tunneling leakage

Subthreshold leakage is a substantial component of total Subthreshold leakage is a substantial component of total leakage power through the 65nm nodeleakage power through the 65nm node

► Leakage variability is another concernLeakage variability is another concern Small variation in linewidth Small variation in linewidth exponential variation in exponential variation in

leakage powerleakage power► Most significant source of leakage variability : Most significant source of leakage variability :

linewidth variationlinewidth variation E.g., in 90nm technology, decrease of linewidth by 10nm E.g., in 90nm technology, decrease of linewidth by 10nm

leakage increases by 5X for PMOS and 2.5X for NMOS leakage increases by 5X for PMOS and 2.5X for NMOS

Linewidth VariationLinewidth Variation► Traditional leakage estimation techniques model Traditional leakage estimation techniques model

linewidth variation as random linewidth variation as random very pessimistic very pessimistic► Reality: Linewidth variation is partly systematic!Reality: Linewidth variation is partly systematic!

► This work: (1) analyze impact of focus variations This work: (1) analyze impact of focus variations (2) improve leakage estimation accuracy (2) improve leakage estimation accuracy (3) (3) optimize leakage accurately optimize leakage accurately (4) reduce pessimistic (4) reduce pessimistic guardbandingguardbanding

Bossung plotBossung plot

Optical Proximity Correction (OPC)Optical Proximity Correction (OPC)

Optical Optical ModelsModels

OPCOPC

Standard cell layoutStandard cell layout

Optical modelsOptical modelswith focus/exposure with focus/exposure conditionsconditions

OPC’ed layoutOPC’ed layout

Focus

Exposure

Process windowProcess window OPC solution validOPC solution valid

OPC solution not validOPC solution not validoutside process windowoutside process window

Linewidth Variation with FocusLinewidth Variation with FocusStandard cell

OPC at nominal defocus

Lithography simulation at nominal defocus

Lithography simulation at 200nm defocus

Printed polysilicon line in yellow shows SIGNIFICANT deviation from drawn for 200nm defocus

Printed polysilicon line in yellow shows NO deviation from drawn for nominal defocus

Sources of Focus VariationSources of Focus Variation► Defocus during lithography is caused primarily due Defocus during lithography is caused primarily due

to wafer topography variation, lens aberration and to wafer topography variation, lens aberration and wafer plane tiltwafer plane tilt Blurring caused by defocus results in lower image Blurring caused by defocus results in lower image

resolution, improper resist development, and linewidth resolution, improper resist development, and linewidth variationvariation

► Wafer topography variation is caused due to Wafer topography variation is caused due to chemical-mechanical polishing (CMP) and shallow chemical-mechanical polishing (CMP) and shallow trench isolation (STI) fill anomalies during wafer trench isolation (STI) fill anomalies during wafer processingprocessing Substrate flatness, films, etc. also contribute to wafer Substrate flatness, films, etc. also contribute to wafer

topographytopographyImperfect wafer planarity after STI CMP

Images print at different defocus levels depending on the topography of the location

Through-Focus Linewidth VariationThrough-Focus Linewidth Variation

► Linewidth variation due to line pitch (Linewidth variation due to line pitch ( “through- “through-pitch”) is compensated by OPC at pitch”) is compensated by OPC at nominal defocusnominal defocus At defocus levels other than nominal, linewidth varies At defocus levels other than nominal, linewidth varies

systematically with pitchsystematically with pitch Dense pitchDense pitch: high density of features within optical : high density of features within optical

radiusradius Isolated pitchIsolated pitch: low density of features within optical : low density of features within optical

radiusradius Linewidth for dense pitches increases with defocus Linewidth for dense pitches increases with defocus

“smiling” “smiling” Linewidth for isolated pitches decreases with defocus Linewidth for isolated pitches decreases with defocus

“frowning”“frowning”► Linewidth variation with pitch and defocus is Linewidth variation with pitch and defocus is

captured in captured in BossungBossung lookup tables lookup tables At any given defocus level, At any given defocus level, linewidth for dense pitches linewidth for dense pitches

is always greater than that of isolated pitchesis always greater than that of isolated pitches

Isolated vs. Dense Linewidth Isolated vs. Dense Linewidth VariationVariation

Portion of a 90nm standard cell layout showing polysilicon lines in isolated, dense and self-compensated contexts

Dense lines “smiling” (linewidth > nominal)

Isolated lines “frowning” (linewidth < nominal)

Self-compensated lines (linewidth ~ nominal)

OutlineOutline

► Systematic Components of Linewidth Systematic Components of Linewidth VariationVariation

► Defocus-Aware Leakage EstimationDefocus-Aware Leakage Estimation ► Experimental StudyExperimental Study► Defocus-Aware Leakage OptimizationDefocus-Aware Leakage Optimization► SummarySummary

Defocus-Aware Leakage Estimation Defocus-Aware Leakage Estimation FlowFlow

► Core idea: Layout analysis Core idea: Layout analysis Defocus-aware Defocus-aware linewidth prediction linewidth prediction leakage estimation leakage estimation

► Flow componentsFlow components Bossung LUT creationBossung LUT creation Pitch calculationPitch calculation Cell leakage estimationCell leakage estimation

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout AnalysisLayout Analysis Placed DesignPlaced Design

Device PitchesDevice Pitches Defocus over DieDefocus over Die

CMP SimulationCMP Simulation

BossungBossungLookup TableLookup Table

Predicted LinewidthsPredicted Linewidths

Leakage Estimation

Bossung Lookup Table CreationBossung Lookup Table Creation

► Done once for a given lithography optical modelDone once for a given lithography optical model► Line-and-space patterns to simulate different line pitchesLine-and-space patterns to simulate different line pitches► Lithography simulation performed in (-200,200)nm defocus Lithography simulation performed in (-200,200)nm defocus

range with 0.38 exposure dose and 0.7 numerical aperturerange with 0.38 exposure dose and 0.7 numerical aperture► Table Rows: pattern informationTable Rows: pattern information► Table Columns: defocus levelTable Columns: defocus level► Table Entries: printed linewidthsTable Entries: printed linewidths

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout AnalysisLayout Analysis Placed DesignPlaced Design

Device PitchesDevice Pitches Defocus over DieDefocus over Die

CMP SimulationCMP Simulation

BossungBossungLookup TableLookup Table

Predicted LinewidthsPredicted Linewidths

Leakage Estimation

Pitch CalculationPitch Calculation

► Device pitch calculation is done usingDevice pitch calculation is done using Location and orientation of standard cellsLocation and orientation of standard cells Device locations within each cell from LVSDevice locations within each cell from LVS

► Device pitch and optical radius used to lookup Device pitch and optical radius used to lookup line-and-space patterns in Bossung tableline-and-space patterns in Bossung table

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout AnalysisLayout Analysis Placed DesignPlaced Design

Device PitchesDevice Pitches Defocus over DieDefocus over Die

CMP SimulationCMP Simulation

BossungBossungLookup TableLookup Table

Predicted LinewidthsPredicted Linewidths

Leakage Estimation

Cell Leakage EstimationCell Leakage Estimation

► Cell leakage estimationCell leakage estimation Cell leakage for each input state estimated by finding Cell leakage for each input state estimated by finding

leaking devices by logic simulationleaking devices by logic simulation► Leakage of stacked devices is neglectedLeakage of stacked devices is neglected

Cell leakage computed using pre-characterized PMOS and Cell leakage computed using pre-characterized PMOS and NMOS leakage tables generated from SPICE simulationNMOS leakage tables generated from SPICE simulation

Estimate is within 5% of cell-level SPICE simulationEstimate is within 5% of cell-level SPICE simulation

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout Analysis Placed Design

Device Pitches Defocus over Die

CMP Simulation

BossungLookup Table

Predicted Linewidths

Leakage Estimation

Layout AnalysisLayout Analysis Placed DesignPlaced Design

Device PitchesDevice Pitches Defocus over DieDefocus over Die

CMP SimulationCMP Simulation

BossungBossungLookup TableLookup Table

Predicted LinewidthsPredicted Linewidths

Leakage Estimation

OutlineOutline

► Systematic Components of Linewidth Systematic Components of Linewidth VariationVariation

► Defocus-Aware Leakage Estimation Defocus-Aware Leakage Estimation ► Experimental StudyExperimental Study► Defocus-Aware Leakage OptimizationDefocus-Aware Leakage Optimization► SummarySummary

Experimental SetupExperimental Setup► Testcases: Testcases: c5315c5315 (2077 cells), (2077 cells), c6288c6288 (4776 cells), (4776 cells), c7552c7552 (3155 cells), (3155 cells),

alu128alu128 (11724 cells) (11724 cells)► Cell library (20 cell) characterization with Cell library (20 cell) characterization with BPTM BSIM3BPTM BSIM3 device models, device models,

Synopsys HSPICESynopsys HSPICE, and , and Cadence SignalStormCadence SignalStorm► Synthesis with Synthesis with Synopsys Design CompilerSynopsys Design Compiler with tight delay constraints. with tight delay constraints.

Placement with Placement with Cadence SoC EncounterCadence SoC Encounter..► OPC, litho-simulation and scattering-bar insertion with OPC, litho-simulation and scattering-bar insertion with Mentor CalibreMentor Calibre

using industry-strength recipes for 100nm linewidth and 193nm stepper.using industry-strength recipes for 100nm linewidth and 193nm stepper.

► Topography used: +100nm Topography used: +100nm at die center, quadratically at die center, quadratically decreases to -100nm at die decreases to -100nm at die cornerscorners

Leakage Estimation ResultsLeakage Estimation Results

0

1

2

3

4

5

6

7

8

9

10

c5315 c7552 c6288 alu128

Testcase

Leak

age

(mW

)

Traditional WC Traditional BC DATO WC

DATO BC DATA WC DATA BC

Spread Reductionc5315: 56%c7552: 49%c6288: 49%alu128: 62%

WC: Worst CaseBC: Best Case

DATO: Defocus-Aware, Topography-ObliviousDefocus Gaussian random with µ=0nm, 3σ=200nm

DATA: Defocus-Aware, Topography-AwareDefocus Gaussian random withµ=predicted topography height3σ=100nm

Per-Instance Leakage EstimationPer-Instance Leakage Estimation

► Ability to predict leakage for each cell instanceAbility to predict leakage for each cell instance

Error distribution of traditionalleakage estimation for c6288 at nominal process corner

Can drive leakage reduction techniques like VCan drive leakage reduction techniques like Vthth assignment, input vector control, gate-length biasing assignment, input vector control, gate-length biasing

E.g., optimize cells that are more leakyE.g., optimize cells that are more leaky

(Negative error Traditional estimate is higher)

OutlineOutline

► Systematic Components of Linewidth Systematic Components of Linewidth VariationVariation

► Defocus-Aware Leakage EstimationDefocus-Aware Leakage Estimation ► Experimental StudyExperimental Study► Defocus-Aware Leakage OptimizationDefocus-Aware Leakage Optimization► SummarySummary

Gate-Length Biasing (Gupta et al. DAC04)Gate-Length Biasing (Gupta et al. DAC04)

► Slightly increase (bias) the Slightly increase (bias) the gate-length (linewidth) of gate-length (linewidth) of devicesdevices Slightly increases delaySlightly increases delay Significantly reduces leakageSignificantly reduces leakage

Bias only the non-critical Bias only the non-critical devicesdevices

► Advantages:Advantages: Reduces runtime leakage and leakage variabilityReduces runtime leakage and leakage variability Can work in conjunction w/ VCan work in conjunction w/ Vthth assignment assignment Gives finer control Gives finer control

over delay-leakage tradeoffover delay-leakage tradeoff Post-layout technique, no additional masks requiredPost-layout technique, no additional masks required

► 15-40% leakage and 30-60% leakage variability reduction 15-40% leakage and 30-60% leakage variability reduction for 90nm with dual-Vfor 90nm with dual-Vthth assignment assignment

► We add defocus-awareness to gate-length biasingWe add defocus-awareness to gate-length biasing

Normalized Delay & Leakage with Gate-Length

00.20.40.60.8

11.2

130

132

134

136

138

140

Gate-Length (nm)

LeakageDelay

Defocus-Aware Gate-Length BiasingDefocus-Aware Gate-Length Biasing► Sensitivity-based greedy opt. in gate-length Sensitivity-based greedy opt. in gate-length

biasingbiasingSensitivity of cell p = ξp = ΔLp×sp

ΔLp : Leakage reduction of cell p upon biasingsp : Timing slack of cell p after biasing it

► Defocus aware sensitivity function:Defocus aware sensitivity function:ξp = ‹ΔLp›×sp

‹ΔLp› : Expected leakage reduction of cell p

► Expected leakage reduction computation:Expected leakage reduction computation:‹ΔLp› = ∑t ‹ΔLpt› ‹ΔLpt› : Exp. leakage reduction of device t of cell pΔLpt = f(lpt) lpt : gate-lengthlpt = g(Dpt, Ppt) Dpt : defocus; Ppt : pitch

‹ΔLpt› = ∑t ∑Df(g(Dpt, Ppt)).P(Dpt) P : probability defocus is Dpt► We assume defocus (D) to be Gaussian randomWe assume defocus (D) to be Gaussian random

Topography-oblivious: Topography-oblivious: µµ=0nm, 3=0nm, 3=200nm=200nm Topography-aware: Topography-aware: µ=topography height, µ=topography height, 33=100nm=100nm

ResultsResults

Leakage after traditional and defocus-aware gate-length biasing

► Optimization for nominal corner and topography mentioned Optimization for nominal corner and topography mentioned earlierearlier

► Modest leakage reductions from 2-7%Modest leakage reductions from 2-7%► 10% optimization runtime increase10% optimization runtime increase

SummarySummary

► Conclusions:Conclusions: Super-linear dependence of leakage on linewidthSuper-linear dependence of leakage on linewidth

pessimism in linewidth pessimism in linewidth large leakage estimation large leakage estimation pessimismpessimism

Proposed approach models pitch- and defocus-dependent Proposed approach models pitch- and defocus-dependent systematic variations.systematic variations.

Significant reduction in leakage estimation spread observed.Significant reduction in leakage estimation spread observed. Improved per-instance leakage estimation Improved per-instance leakage estimation use in leakage use in leakage

reduction approaches.reduction approaches. Defocus awareness in gate-length biasing improves leakage Defocus awareness in gate-length biasing improves leakage

reduction by 2-7%.reduction by 2-7%.

► Future WorkFuture Work Include other sources of systematic variation like lens Include other sources of systematic variation like lens

aberrations.aberrations. Consider systematic impact on timing also while Consider systematic impact on timing also while

optimization.optimization.

Thank You!

Questions?