Double Patterning-Aware Extraction and Static Timing Analysis Flows For Digital Design Sign-Off in 20/14nm Tamer Ragheb, Steven Chan, Adrian Au Yeung, and Richard Trihy Design Methodology CAD Team June 2-6, 2013

Outline Why Double Patterning (DPT)? DPT Mask Misalignment Modeling in Parasitic Extraction Different DPT Extraction Flows Parasitic Extraction/STA Analysis on P&R Design Blocks Recommended 20/14nm Extraction/STA Block-Level Sign-Off Flow November 8, 2018

Why Double Patterning (DPT)? 20nm needs 64nm BEOL min. Pitch for scaling Delay in readiness of next generation lithography (NGL) BEOL min. pitch = 2.λsource.k1 / NA λsource =193nm / NA=1.35 / k1 is the process coefficient =0.25 (difficult printability) Min. Pitch ~ 72nm with one mask  Solution: Double Patterning Technology DPT utilizes the existing lithography intelligently Most commonly adopted approach is a litho-etch, litho-etch (LELE) Pros: Achieves 64nm pitch needed / Relaxes k1 coeff (better and more reliable litho) Cons: Can’t guarantee 100% accuracy in overlaying the two masks There are other techniques for double patterning such as litho-freeze, litho-etch (LFLE) and self-aligned double patterning (SADP) LELE achieves the best compromise between cost, processing, and yield Decomposition Two Masks One Mask November 8, 2018

DPT Misalignment Modeling Techniques: Mask Shift Two common approaches for DPT misalignment modeling: Mask shift flow Actually shifts one mask with respect to the other mask in XY directions Pros: Accurate if the mask misalignment on silicon is known (value & direction) Cons: Requires coloring or decomposing the design Requires designer to specify exact mask shift amount and direction for each DPT layer Determining worst case impact on timing requires 2N different shifts extractions per RC corner, where N is the number of DPT layers Mask shift flow let the DPT-aware extraction tool process the layout to actually shift one mask relative to the other (accurate results) It requires a fully decomposed (colored) design which means extra steps and major changes in the flows as compared to 28nm flow It requires a lot of trials to find the worst case condition (2^N different shifts for each shift value, where N is the number of DPT levels) It requires more trials if one assumes different shift value on each level November 8, 2018

DPT Misalignment Modeling Techniques: DPT Corner Two common approaches for DPT misalignment modeling: DPT corner flow Models mask misalignment as change in dielectric constant (ER_VS_SI_SPACING) Pros: Bounds mask misalignment effect Supports both colorless (non-decomposed) and colored (decomposed) flows Requires almost no changes to existing sign-off flows Cons: Can be pessimistic with respect to a real mask shift (assume change in space on both sides) DPT corner flow represents an approximation of the electrical effects of real physical mask shift Increases dielectric constant to represent a shift towards the neighbour (smaller space) Decreases dielectric constant to represent a shift far from the neighbour (larger space) This table is characterized using Raphael Simulations on test structures. It provides a seamless transition for designers from 28nm flows to 20nm/14nm flows since it requires almost no change to existing sign-off flows November 8, 2018

Full or selective coloring Different DPT-aware Extraction Flows Full or selective coloring November 8, 2018

Outline Why Double Patterning (DPT)? DPT Mask Misalignment Modeling in Parasitic Extraction Different DPT Extraction Flows Parasitic Extraction/STA Analysis on P&R Design Blocks Recommended 20/14nm Extraction/STA Block-Level Sign-Off Flow November 8, 2018

DPT Extraction/STA of P&R Design Blocks SIMD multi-media engine from a high-frequency CPU core Std cell count ~150K / Freq > 1.25GHz / with > 85% std cell utilization Routing on M2-M7 (M1 is reserved for standard cells only) Three different BEOL stack options used 3Mx: 3 DPT levels (baseline for comparison) 3Mx_dense: 3 DPT levels but denser than 3Mx 6Mx: 6 DPT levels For each of the 3 BEOL variants, we ran 13 different Extraction/STA flows Analyzed change in capacitance distribution / overall impact on timing & Frequency Extraction Flow Corner/Shift Decomposition Colored_DPmax DPT corner DPmax Fully-decomposed Colorless_DPmax Non-decomposed Shifts 1-4 Mask shift 4 Typical shifts (±x, ±y) Shifts 5-8 4 Maximum shifts (±x, ±y) Colored_DPmin DPmin Colorless_DPmin No DPT modeling Traditional We needed to study DPT misalignment effect on real design like a SIMD engine from ARM Cortex A9 We used 3 different BEOL stacks to study the DPT effect on different routing density and different number of DPT levels We will compare mask shifts in different directions and different shift values to the DPT corners flow results in both colorless and colored flows And to make the analysis complete, we will compare the effect on capacitance and then on the timing of the design using STA analysis November 8, 2018

Findings from Capacitance distributions Direction of mask shift is NOT important Statistically, shift value is more important Shift direction is important for specific paths (2N different combination/shift value) Both colored and colorless DPT corners/flows have similar results DPT corners bound ALL shifts DPT effect increases by increasing routing density & #of DPT layers Max. Shifts From the statistical distribution of total capacitance change due to each mask shift or DPT corner (assuming No_Shift situation as the reference for the analysis), we found that: Shifts 1-4 are typical shift value in different directions. We represented them as one curve because all the curves were almost exactly the same. The same for shifts 5-8 with max. shift value. The direction of shift does not matter as much when one looks at the full design but it is important for specific path study as we will see in later slides The DPT effect increases by increasing the density similar to SI effects. However, increasing number of DPT levels increases the DPT effect dramatically. Both colored and colorless DPT corners give almost the same mean results but colorless flow gives wider variance since it is more pessimistic (applies DPT effects every where) DPT corners bound nicely almost all the shift situations Typical Shifts November 8, 2018

Findings from STA Results: WNS Using the freq change in the slowest path “IP Freq” Direction of mask shift is important when we study just one path in STA Both colored and colorless DPT corners have similar results (timing difference within noise) DPT corners bound most mask shifts (all Typical shifts & most Max. shifts) From the STA results of the timing of worst path only in each situation due to each mask shift or DPT corner (assuming No_Shift situation as the reference for the analysis), we found that: Since it is only one path, then direction can matter (compare shift7 vs shifts 5,6,8) The DPT effect increases dramatically by increasing number of DPT levels (>3X effect) Both colored and colorless DPT corners give almost the same results DPT corners bound nicely almost all the shift situations Worst Negative Slack Path November 8, 2018

DPT effect w/o SI-aware routing DPT effect w/ SI-aware routing SI-aware Routing & Hold Time analysis DPT effect decreases by applying SI-aware routing ~50% reduction in DPT effects All our results with SI-aware routing DPT effect on Hold time is minimal due to: Short data paths – not much DPT effect Clock skew induced race conditions possible But DPT effect on clock skew is very small Most clock routes are not on DPT layers Clock is routed with 2w/2s NDRs – less impact Stack DPT effect w/o SI-aware routing DPT effect w/ SI-aware routing 3Mx ~X% <0.5X% 3Mx_dense ~Y% <0.7Y% 6Mx ~Z% ~0.5Z% As we discussed before that DPT can be considered as SI (Signal Integrity effect), therefore using SI-aware routing can reduce the DPT misalignment effect by ~50% All previous analyses were setup timing, but studying Hold timing, we found that DPT effect is minimal due to the layout nature of clock routes and short data paths November 8, 2018

Outline Why Double Patterning (DPT)? DPT Mask Misalignment Modeling in Parasitic Extraction Different DPT Extraction Flows Parasitic Extraction/STA Analysis on P&R Design Blocks Recommended 20/14nm Extraction/STA Block-Level Sign-Off Flow November 8, 2018

Extraction Corners Recommendations 5 traditional corners with mask_shift enabled Cmax / Cmin / Nominal / RCmax / RCmin Enable mask shift to analyze DPT effect on specific paths if needed Recommended 4 DPT corners for most P&R designs and flows 4 DPT corners expand the BEOL space to account for mask misalignment CmaxDPmax / RCmaxDPmax / CminDPmin / RCminDPmin CmaxDPmax CminDPmin RCmaxDPmax RCminDPmin Cmax As a conclusion, we recommend designers to apply the same five corners methodology but with replacing 4 green corners with 4 red ones (DPT-aware corners)  No increase in number of corners used That will increase slightly the design corners coverage to include DPT effects and shield designers from this added complexity We also provide Mask Shift capability just in case any designer needs to study DPT effects on a certain specific path and willing to go through the extra time and efforts We recommend DPT colorless flow due to its simplicity (does not need a colored GDS/database) and the close results it produces relative to DPT colored flow and Mask Shift flow No change needed in STA CAD flow and it showed small impact of DPT effects on setup timing as a function of routing density and number of DPT levels. However, DPT has minimal effect on Hold timing C RCmin Nominal RCmax Cmin R November 8, 2018

Extraction and STA Flow Recommendations Extraction Flow: Use colorless flow with DPT corners – no change needed to existing CAD flow STA Flow: No change needed to existing CAD flow – small impact on setup time due to DPT PEX corners, almost no impact on hold time Recommend Option 1a for most designs November 8, 2018

Q & A November 8, 2018

DPT Extraction of Simple Structures Using an interdigitized simple dense interconnect structure: Varying #of lines @min pitch from 2-20 lines Mask shift flow is our golden reference of accuracy Gives exactly same results as Manual layout shift Shifts “E2” mask in the GDS layout to the right/left relative to “E1” mask DPT corner flow: uses DPmax and DPmin extraction corners Compare DPT corner flow to the mask shift flow to analyze extraction accuracy ……… These two simple structures represent most of the situations in real designs (dense symmetrical designs and asymmetrical sparse designs). Manual shift is our base for comparison and it is done by shifting one mask relative to the other in the layout to capture what we expect to have on silicon from DPT misalignment Mask shift flow is letting the DPT-aware extraction tool to do the mask shift based on value and direction that we enter. We found that the mask shift flow gives EXACTLY the same results as manual shift, so we will use it as the golden reference for us through this work And then we compare the DPT corner flow to the mask shift flow under different scenarios November 8, 2018

DPmax and DPmin are good bounds DPT Extraction of Simple Structures: Results Observations: For #of interconnects >4, DPmax and DPmin provide good bounds DPmin corner bound not as tight on symmetric dense structures due to corner cases Case of 2 lines: Usually does not exist in real designs due to metal fill Case of 4 lines: Still one edge is direction sensitive but well bounded by DPmax & DPmin In case of Symmetrical structure, for any odd number of interconnects or even number > 4, the mask shift effect can be bounded between the No_Shift and Dpmax corner. Here the Dpmin corner is over estimating the reduction of coupling capacitance since almost all shifts are worse that No_shift situation But we need the Dpmin corner for the asymmetrical case as we will see in the next slide Y-axis is NOT %cap DPmax and DPmin are good bounds November 8, 2018