DefocusAware Leakage Estimation and Control Andrew B Kahng
Defocus-Aware Leakage Estimation and Control Andrew B. Kahng†‡ Swamy Muddu‡ Puneet Sharma‡ CSE† and ECE‡ Departments, UC San Diego
Outline ► Systematic Components of Linewidth Variation ► Defocus-Aware Leakage Estimation ► Experimental Study ► Defocus-Aware Leakage Optimization ► Summary
Leakage Power Leakage power limits large, high-performance designs in sub-100 nm regime ► Decreasing threshold voltages (Vth) boost performance but increase leakage ► Components of leakage power ► § § § ► Subthreshold leakage Gate leakage Band-to-band tunneling leakage Subthreshold leakage is a substantial component of total leakage power through the 65 nm node Leakage variability is another concern § Small variation in linewidth exponential variation in leakage power ► Most significant source of leakage variability : linewidth variation § E. g. , in 90 nm technology, decrease of linewidth by 10 nm leakage increases by 5 X for PMOS and 2. 5 X for NMOS
Linewidth Variation Traditional leakage estimation techniques model linewidth variation as random very pessimistic ► Reality: Linewidth variation is partly systematic! ► Bossung plot ► This work: (1) analyze impact of focus variations (2) improve leakage estimation accuracy (3) optimize leakage accurately (4) reduce pessimistic guardbanding
Optical Proximity Correction (OPC) Standard cell layout OPC Optical Models OPC’ed layout Optical models with focus/exposure conditions Exposure Process window OPC solution valid Focus OPC solution not valid outside process window
Linewidth Variation with Focus Standard cell OPC at nominal defocus Lithography simulation at 200 nm defocus Printed polysilicon line in yellow shows SIGNIFICANT deviation from drawn for 200 nm defocus Printed polysilicon line in yellow shows NO deviation from drawn for nominal defocus
Sources of Focus Variation ► Defocus during lithography is caused primarily due to wafer topography variation, lens aberration and wafer plane tilt § Blurring caused by defocus results in lower image resolution, improper resist development, and linewidth variation ► Wafer topography variation is caused due to chemicalmechanical polishing (CMP) and shallow trench isolation (STI) fill anomalies during wafer processing § Substrate flatness, films, etc. also contribute to wafer topography Imperfect wafer planarity after STI CMP Images print at different defocus levels depending on the topography of the location
Through-Focus Linewidth Variation ► Linewidth variation due to line pitch ( “throughpitch”) is compensated by OPC at nominal defocus § At defocus levels other than nominal, linewidth varies systematically with pitch § Dense pitch: high density of features within optical radius § Isolated pitch: low density of features within optical radius § Linewidth for dense pitches increases with defocus “smiling” § Linewidth for isolated pitches decreases with defocus “frowning” ► Linewidth variation with pitch and defocus is captured in Bossung lookup tables § At any given defocus level, linewidth for dense pitches is always greater than that of isolated pitches
Isolated vs. Dense Linewidth Variation Portion of a 90 nm standard cell layout showing polysilicon lines in isolated, dense and selfcompensated contexts Self-compensated lines (linewidth ~ nominal) Dense lines “smiling” (linewidth Isolated lines “frowning” > nominal) (linewidth < nominal)
Outline ► Systematic Components of Linewidth Variation ► Defocus-Aware Leakage Estimation ► Experimental Study ► Defocus-Aware Leakage Optimization ► Summary
Defocus-Aware Leakage Estimation Flow Layout. Analysis Layout Placed Design Placed Device Pitches CMPSimulation CMP Defocusover Die Defocus Die Bossung Lookup. Table Predicted. Linewidths Predicted Leakage Estimation Core idea: Layout analysis Defocus-aware linewidth prediction leakage estimation ► Flow components ► § Bossung LUT creation § Pitch calculation § Cell leakage estimation
Bossung Lookup Table Creation Layout. Analysis Layout Placed Design Placed Device Pitches CMPSimulation CMP Defocusover Die Defocus Die Bossung Lookup. Table Predicted. Linewidths Predicted Leakage Estimation ► ► ► Done once for a given lithography optical model Line-and-space patterns to simulate different line pitches Lithography simulation performed in (-200, 200)nm defocus range with 0. 38 exposure dose and 0. 7 numerical aperture Table Rows: pattern information Table Columns: defocus level Table Entries: printed linewidths
Pitch Calculation Layout. Analysis Layout Placed Design Placed Device Pitches CMPSimulation CMP Defocusover Die Defocus Die Bossung Lookup. Table Predicted. Linewidths Predicted Leakage Estimation ► Device pitch calculation is done using § Location and orientation of standard cells § Device locations within each cell from LVS ► Device pitch and optical radius used to lookup lineand-space patterns in Bossung table
Cell Leakage Estimation Layout. Analysis Layout Placed Design Placed Device Pitches CMPSimulation CMP Defocusover Die Defocus Die Bossung Lookup. Table Predicted. Linewidths Predicted Leakage Estimation ► Cell leakage estimation § Cell leakage for each input state estimated by finding leaking devices by logic simulation ► Leakage of stacked devices is neglected § Cell leakage computed using pre-characterized PMOS and NMOS leakage tables generated from SPICE simulation § Estimate is within 5% of cell-level SPICE simulation
Outline ► Systematic Components of Linewidth Variation ► Defocus-Aware Leakage Estimation ► Experimental Study ► Defocus-Aware Leakage Optimization ► Summary
Experimental Setup ► ► ► Testcases: c 5315 (2077 cells), c 6288 (4776 cells), c 7552 (3155 cells), alu 128 (11724 cells) Cell library (20 cell) characterization with BPTM BSIM 3 device models, Synopsys HSPICE, and Cadence Signal. Storm Synthesis with Synopsys Design Compiler with tight delay constraints. Placement with Cadence So. C Encounter. OPC, litho-simulation and scattering-bar insertion with Mentor Calibre using industry-strength recipes for 100 nm linewidth and 193 nm stepper. Topography used: +100 nm at die center, quadratically decreases to -100 nm at die corners
Leakage Estimation Results WC: Worst Case BC: Best Case DATO: Defocus-Aware, Topography-Oblivious Defocus Gaussian random with µ=0 nm, 3σ=200 nm DATA: Defocus-Aware, Topography-Aware Defocus Gaussian random with µ=predicted topography height 3σ=100 nm Spread Reduction c 5315: 56% c 7552: 49% c 6288: 49% alu 128: 62%
Per-Instance Leakage Estimation ► Ability to predict leakage for each cell instance Error distribution of traditional leakage estimation for c 6288 at nominal process corner (Negative error Traditional estimate is higher) Can drive leakage reduction techniques like Vth assignment, input vector control, gate-length biasing E. g. , optimize cells that are more leaky
Outline ► Systematic Components of Linewidth Variation ► Defocus-Aware Leakage Estimation ► Experimental Study ► Defocus-Aware Leakage Optimization ► Summary
Gate-Length Biasing (Gupta et al. DAC 04) ► Slightly increase (bias) the gate-length (linewidth) of devices § Slightly increases delay § Significantly reduces leakage Bias only the non-critical devices ► Advantages: § Reduces runtime leakage and leakage variability § Can work in conjunction w/ Vth assignment Gives finer control over delay-leakage tradeoff § Post-layout technique, no additional masks required 15 -40% leakage and 30 -60% leakage variability reduction for 90 nm with dual-Vth assignment ► We add defocus-awareness to gate-length biasing ►
Defocus-Aware Gate-Length Biasing ► Sensitivity-based greedy opt. in gate-length biasing Sensitivity of cell p = ξp = ΔLp×sp ΔLp : Leakage reduction of cell p upon biasing sp : Timing slack of cell p after biasing it ► Defocus aware sensitivity function: ξp = ‹ΔLp›×sp ‹ΔLp› : Expected leakage reduction of cell p ► Expected leakage reduction computation: ‹ΔLp› = ∑t ‹ΔLpt› : Exp. leakage reduction of device t of cell p ΔLpt = f(lpt) lpt : gate-length lpt = 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 random § Topography-oblivious: µ=0 nm, 3 =200 nm § Topography-aware: µ=topography height, 3 =100 nm
Results Leakage after traditional and defocus-aware gate-length biasing Optimization for nominal corner and topography mentioned earlier ► Modest leakage reductions from 2 -7% ► 10% optimization runtime increase ►
Summary ► Conclusions: § Super-linear dependence of leakage on linewidth pessimism in linewidth large leakage estimation pessimism § Proposed approach models pitch- and defocus-dependent systematic variations. § Significant reduction in leakage estimation spread observed. § Improved per-instance leakage estimation use in leakage reduction approaches. § Defocus awareness in gate-length biasing improves leakage reduction by 2 -7%. ► Future Work § Include other sources of systematic variation like lens aberrations. § Consider systematic impact on timing also while optimization.
Thank You! Questions?
- Slides: 24