1. Study of Floating Fill Impact on Interconnect Capacitance Andrew B. Kahng Kambiz Samadi Puneet Sharma CSE and ECE Departments University of California, San Diego

2. Outline Introduction Foundations Study of Capacitance Impact of Fill –Proposed Guidelines Validation of Guidelines Conclusions

3. Introduction Why fill is needed? Planarity after chemical-mechanical polishing (CMP) depends on pattern Metal fill reduces pattern density variation Stringent planarity requirements  fill mandatory now Impact on capacitance Grounded fill Increases capacitance  larger delay Shields neighboring interconnects  reduced xtalk Floating fill Increases coupling capacitance  significantly more xtalk  signal integrity & delay Increases total capacitance  larger delay

4. Motivation Floating-fill extraction is complex Floating-fill capability recently added to full-chip extractors In past large buffer distance design-rule used Reduces coupling impact Density constraints cannot be met  reduce buffer distance  inaccuracy in capacitance estimation We systematically analyze capacitance impact of fill config. parameters (e.g., fill size, fill location, interconnect width, etc.) Propose guidelines for floating fill insertion to reduce capacitance impact Grounded fill used despite disadvantages (e.g., higher delay impact, routing needed) Designers use floating fill extremely conservatively  Better understanding of capacitance impact needed

5. Assumptions & Terminology Same-layer analysis –Fill affects coupling of all interconnects in proximity –We study effect on coupling capacitance of same-layer interconnects  simplifies analysis Terminology –Fill and coupling interconnects are on Layer M (layer of interest) –i a and i b are interconnects of interest with coupling C ab –We study increase in coupling ΔC ab due to fill insertion –Dimensions measured in tracks (=0.3µ) –Usability not compromised because: 1.Coupling with same-layer neighbor large –Validation: multiple configs with different densities on different layers considered 2.Fill insertion between two same-layer interconnects, increases coupling significantly –Validation: fill inserted everywhere  Large fraction of coupling impact captured by same-layer analysis Synopsys Raphael, 3D field solver, used in all experiments

6. Outline Introduction Foundations Study of Capacitance Impact of Fill –Proposed Guidelines Validation of Guidelines Conclusions

7. Foundation 1 Experimental Setup Two interconnects on Layer M separated by three tracks Fill inserted on Layer M between two interconnects M+1/M-1 density is set to 33% 20%, 33%, 100% metal density for Layer M+2/M-2 tried For ΔC ab analysis, Layers M-2 and M+2 may be assumed as groundplanes

8. Foundation 2 Experimental Setup Two interconnects on Layer M separated by three tracks M+1 & M-1 density is set to 33% M+2 & M-2 assumed groundplanes Fill features inserted on Layer M at different locations ΔC ab is affected by fill geometries in the region RE ab only.

9. Outline Introduction Foundations Study of Capacitance Impact of Fill –Proposed Guidelines Validation of Guidelines Conclusions

10. Fill Size Fill length (along the interconnects) Linear increase in ΔC ab with Y-intercept Guideline: Increase fill length instead of width Fill width Increases super-linearly Using parallel-plate capacitor analogy, 1/w relation expected Settings: Interconnect separation = 3 tracks Layers M-1/M+1 have 33% density 2 track width, 1 track length

11. Interconnect Spacing ΔC ab decreases super-linearly with spacing For larger spacings (>10 tracks), coupling with M-1 and M+1 wires more significant Settings: Fill size = 2 tracks x 2 tracks Layers M-1/M+1 have 33% density Guideline: Insert fill where wire spacing is large

12. Fill Location Y-axis translation C ab unaffected until fill close to an interconnect ending Guideline: Center fill horizontally between interconnects X-axis translation ΔC ab increases ~linearly Capacitance between fill & closer interconnect increases dramatically Settings: Wire spacing = 8 tracks Fill size = 2 tracks wide, 4 long Layers M-1/M+1 have 33% density

13. Edge Effects Study two cases: (1) two interconnects horizontally aligned, and (2) not horizontally aligned With Y-axis translation of fill, edge effects observed When fill no longer in R ab, ΔC ab dramatically decreases Settings: Layers M-1/M+1 have 33% density Interconnect width = 2 tracks Fill size = 4 tracks long, 2 wide Guideline: Insert fill in low-impact region (= outside R ab ) R ab

14. Interconnect Width Change width of one interconnect Interconnect-fill spacing and interconnect spacing constant ΔC ab increases rapidly, but saturates at ~ 4 tracks Guideline: Insert fill next to thinner interconnects

15. Multiple Columns Vertically aligned fill geometries are said to be in a fill column Change number of fill columns in fill pattern Fill area is kept constant ΔC ab reduces with number of fill columns Cf. Tran. Electron Devices ’98 (MIT) Cf. VMIC-2004 invited paper (UCSD / UCLA) Guideline: Increase number of fill columns

16. Multiple Rows Horizontally aligned fill geometries are said to be in a fill row Change number of fill rows in fill pattern Fill area is kept constant ΔC ab increases with number of fill rows As spacing between two fill rows decreases, the ΔC ab decreases Guideline: Decrease number of fill rows and inter-row spacing

17. Outline Introduction Background & Terminology Study of Capacitance Impact of Fill –Proposed Guidelines Validation of Guidelines Conclusions

18. Application of Guidelines RegularStaggeredWith guidelines Guidelines applied 1.Edge effects 2.Maximize columns 3.Minimize rows 4.Centralize fill ΔC = 64% ΔC = 62% ΔC = 16% Apply guidelines on 3 interconnect configurations Reasonable design rules assumed Configuration 1

19. Guidelines on Configuration 2 ΔC = 41% ΔC = 30% Guidelines applied 1.Wire width 2.Minimize rows

20. Guidelines on Configuration 3 ΔC = 27% ΔC = 11% Guidelines applied 1.High-impact region 2.Edge effects 3.Wire spacing 4.Minimize rows 5.Centralize fill

21. Conclusions Coupling with same-layer neighboring wires significant and same-layer fill insertion increases it dramatically Systematically analyzed the impact of floating fill configurations on coupling of same-layer interconnects Propose guidelines for floating fill insertion to reduce coupling increase Ongoing work: –3D extensions: Impact on coupling of different-layer interconnects –Timing- and SI-driven fill insertion methodology