1. 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

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. Q & A
November 8, 2018

16. DPT Extraction of Simple Structures
Using an interdigitized simple dense interconnect structure:
Varying #of 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

17. 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