Accurate Signoff with Advanced Variation Methodology Ayhan Mutlu Synopsys Co., Ltd. Moonsu Kim, Eun yeung Yu, Eunbyeol Kim Samsung Electronics Co., Ltd. System LSI Division

Motivation Process & Design trends Random variation is increasing in advanced process nodes Design size and performance gap are also increasing, but TAT limit is almost constant Requirement for process variation aware STA Advanced node requires higher level of STA accuracy for better PPA within tight TAT limit Accurate process variation will remove unnecessary pessimism and optimism at the same time Traditional AOCV(Advanced On Chip Variation) and constraint variation modeling has limitations resulting in inherent pessimism Need to use POCV (Parametric OCV) to resolve traditional method’s limitation using advanced modeling for delay/slew/constraint variation In this slide, I want to introduce the motivation of this presesentation about ‘why accurate process variation aware STA is requried’ As shown in right graph, performance gap between realistic and requirement is increased linearly according to process nodes. As shown in left graph, design size trend is similarly changed according to process advance. Considering this trend, requirement for higher level of STA accuracy for better PPA within tight TAT limit becomes greater than before. By this, accurate process variation will remove unnecessary pessimism and optimism at the same time. We have traditional AOCV flow and constraint variation modeling but they have inherent pessimism. This is a big motivation why we developed POCV flow using advanced modeling for delay/slew/constraint variation.

How to improve accuracy of process variation STA? Challenge 1: slew/load impact to delay variation In Advanced OCV (AOCV), delay variation is function of logic depth and distance, but does not consider slew/load impact In actual design, the magnitude of process variation will increase at higher slew/load indices on advanced nodes AOCV Variation is independent to slew/load AOCV Variation is dependent on stage count As shown in the left graph, In AOCV, delay variation is function of logic depth and distance but doesn’t consider slew/load impact. But in actual design, the magnitude of process variation will increase at higher slew/load indices on advanced nodes. Conventional STA with AOCV can’t consider slew/load impact to delay variation. The magnitude of process variation will increase at higher slew/load indices on advanced nodes as shown in the left graph In actual design, there are various slew/load situation. Challenges - How can we provide good & accurate STA? OCV_sigma (AOCV)

Delay Variation Needs to Be Slew/Load Dependent Solution: Liberty Variation Format (LVF) for slew/load-based variation LVF includes delay variation based on actual slew/load The cell delay variation is modeled as a function of input transition and output load per timing arc POCV LVF delay variation σ = f (slew,load) X1 X2 X3 Propagated path arrival time distribution X1+ X2+X3 EXAMPLE of LVF delay variation ocv_sigma_cell_rise ("delay_template_4x4") { sigma_type : "late"; index_1("0.001, 0.005, 0.010, 1.00"); index_2("0.001, 0.002, 0.003, 0.10"); values( "σ11, σ12, σ13, σ14", \ "σ21, σ22, σ23, σ24", \ "σ31, σ32, σ33, σ34", \ "σ41, σ42, σ43, σ44", ); } LVF(Liberty Variation Format) is a good solution for challenge1. LVF includes delay variation is modeled as a function of input transition and output load per timing arc. During POCV STA, distribution of arrival time is assumed as gaussian and calculated by propagating and accumulating each cell’s variation. Slew Load

Delay Variation Needs to Be Slew/Load Dependent Samsung experiment results Extracted 300 paths from real design to compare arrival times using PrimeTime POCV with MonteCarlo (MC) reference POCV has good correlation with MC using slew/load dependent model AOCV has large pessimism for some cases and therefore larger error spread than POCV POCV error AOCV average -0.16% -0.85% stdev 1.02% 7.45% We tried an experiment to show slew/load aware process variation impact. We extracted 300 paths from real design to compare arrival times using Primetime POCV with MC. POCV has good correlation with MC, on the other hand AOCV from lumped slew/load model has large pessimism for some cases and therefore larger error spread than POCV. POCV has smaller average error than AOCV. And we can see narrower spread of POCV error than AOCV by comparing stdev values. AOCV(green) : lumped slew/load model POCV(red) : slew/load aware variation model Monte Carlo(blue): reference

How to improve accuracy of process variation STA? Challenge 2: Common point optimism reduction for Min Pulse Width(MPW) and half-cycle path Different transition at common point  need to keep process variation at common point In AOCV, process variation can’t be exactly calculated by statistical sum of rising and falling paths and it can’t be separated with other variation models  Process variation will be removed from slack computation C A B cell1 cell2 A B C ------------------------------ Launch clock : F  R  F Capture clock: R  F  R The other challenge #2 is common point optimism in the min pulse width and half-cycle path. In those types of timing paths, there are different transitions at common point and this means actually launch path clock has different transistor path(F@A--> R@B  F@C) with capture path (R@A--> F@B  R@C). In the AOCV based variation at common point C can be optimistic as it may be removed by CRPR. But Actual process variation at Point C should be RSS between Launch and capture paths’ variations. AOCV-based variation at point C = max_derate – min_derate (CRPR) = 0 (max_derate = min_derate) Actual process variation at Point C = sqrt( σcell1,rise^2+σcell2,fall^2+σcell1,fall^2+σcell2,rise^2 ) v.s. AOCV-based variation can be optimistic as it may be removed by CRPR

Common Point Optimism Reduction in MPW Solution: Accurate process variation for MPW using POCV Using POCV, accurate process variation for MPW and half cycle’s slack computation will remove optimism Samsung experiment results For extracted 10K paths from real design, average 3.3% optimism reduction can be reflected into MPW slack (or half cycle path) computation by POCV model POCV process variation at Point C (same as actual) = sqrt( σcell1,rise^2+σcell2,fall^2+σcell1,fall^2+σcell2,rise^2 ) C A B cell1 cell2 A B C ------------------------------ Launch clock : F  R  F Capture clock: R  F  R avg stdev MPW Delta -3.32% 0.79% Solution for challenge #2 can be resolved by POCV because Process variation’s are modeled in LVF per each timing arc(rising/falling). By Using POCV, we can remove optimism for this case by computing accurate process variation for MPW and hal cycle CRPR. We tested this with real design and average 3.3% optimism reduction from 10K paths in min pulse with slack. < MPW Delta: Optimism Reduction> Delta = (new_pw – old_pw) / old_pw new_pw: pulse width considering process variation at common point using POCV old_pw: pulse width not considering process variation (traditional)

How to improve accuracy of process variation STA? Challenge 3: Delay variation is highly correlated with output slew variation Output slew variation will affect delay variation in next stage Output slew variation has an increased impact at lower voltage MonteCarlo Simulation for Inverter Cell ? Dσcell2 ? Sσcell2 Highly correlated Dσcell1 Sσcell1 X axis: cell delay Y axis: output slew Highly correlated ρ = 0.78 Sin,cell2 ^ cell1 cell2 Dσcell1: cell1’s delay variation Sσcell1 : cell1’s output slew variation S in,cell1 : cell2’s input slew Challenge #3 is how to deal slew variation impact on delay variation? Actually, delay variation is highly correlated with output slew variation like below right side figures. And output slew variation will be propagated to next cell’s input. Therefore we can guess slew variation at cell1 will affect cell2’s variation also.

Consider Correlation between Slew and Delay variation Solution: POCV considers correlation between slew and delay variation Better accuracy for lower voltages by reflecting correlation between slew and delay variation in STA Samsung experiment results About 1% accuracy improvement by correlated slew variation modeling for 150 extracted paths <POCV> Correlated delay and slew variation Dσcell2 Dσcell2(Sσcell1) Sσcell2 Sσcell2 (Sσcell1) Dσcell1 Sσcell1 Dσcell1: cell1’s delay variation w/o input slew variation Sσcell1 : cell1’s output slew variation Dσcell2 : cell2’s delay variation w/o input slew variation Dσcell2(Sσcell1) : cell2’s delay variation induced by input slew variation Sσcell2 : cell2’s output slew variation w/o input slew variation Sσcell2 (Sσcell1) : cell2’s output slew variation induced by input slew variation ^ cell1 cell2 In POCV, this slew variation can be considered with its correlation with delay variation. In this figure, cell2’s variation is partially correlated with cell1 and this partial correlation impact can be separated from pure independent random variation (Dsigma_cell2) and modeled as function of Ssigma_cell1 which is Dsigmacell2(Ssigmacell1). PT does same way to consider cell1’ slew variation impact on cell2’s slew variation which is Ssigmacell2 function of Ssigma cell1. By considering this partial correlation induced by slew variation, we have 1% accuracy improvement comparing with MC simulation. This table shows there cases of POCV error comparing with Montecalro simulation. In the delay variation only case, we have average 1.6% error but this will be reduced to 0.84% by considering slew variation. But this case2 doesn’t consider partial correlation relation between slew and delay. Like third case which consider this correlation, we have 0.56% average error. Delay variation only Delay variation + slew variation (no correlation) variation (correlated) Error(%) = (STA –MC)/MC Mean =1.55% Stdev = 0.70% Mean =0.84% Stdev = 0.56% Mean = 0.56% Stdev = 0.55%

How to improve accuracy of process variation STA? Challenge 4: Traditionally, Flop’s constraint variation is added to nominal constraint value as margin  Delay variation and constraint variation in STA becomes linear sum However, delay variation and constraint variation is independent and not correlated  Delay variation and constraint variation should be statistical sum By separating constraint variation with nominal constraint value  theoretically maximum 40% pessimism reduction A) Traditional linear sum: total variation = σpath + σH B) POCV Statistical sum: total variation = SQRT ( σpath^2 + σH^2) where σpath = SQRT ( σL^2 + σC^2) Max difference between linear and statistical sum is when σpath= σH  Max { (A–B) / B } = (2 - 1.414) / 1.414 = ~40%  This is the pessimism from linear sum method By adopting separate constraint variation model, maximum 40% pessimism of slack variation can be reduced σL σC σH

Statistical Modeling of Constraint Variation Solution: POCV Support of Constraint Variation Uses statistical sum of delay and constraint variation Theoretical maximum of 40% pessimism reduction than traditional method Samsung experiment results Extracted 1000 paths from real design to evaluate real world pessimism reduction when using separate modeling of FF constraint variation Linear sum pessimism = (linear sum slack – statistical sum slack)/linear sum slack Max ~40% pessimism reduction Majority of paths achieve close to 40% pessimism reduction in total variation Average 37% pessimism reduction of 1000 paths avg stdev Linearsum Pessimism -0.37 0.04

Summary Review potentially opportunities to improve accuracy challenges caused by limitation of traditional variation (AOCV) and review solutions using advanced method of PrimeTime POCV Slew/load aware delay variation modeling Accuracy improvement  more opportunity of both robust and optimized design based on PBA accuracy enhancement Common point optimism removal for Half-cycle and Min Pulse Width Average 3.3% optimism reduction  robust design for MPW and half cycle path Correlated slew variation impact on accuracy Average 1% mean accuracy improvement by correlated modeling of delay and slew variation Statistical constraint variation modeling Average 37% pessimism reduction compared to traditional linear sum of delay variation and constraint variation POCV based accurate analysis is necessary to meet tight PPA requirement with limited resources for advanced nodes Results shown in this presentation based on Samsung Advanced node design using Synopsys PrimeTime POCV Analysis From this accuracy enhancement, we have more chance to optimize design.