1. 14 February, 2004SLIP, 2004 Self-Consistent Power/Performance/Reliability Analysis for Copper Interconnects Bipin Rajendran, Pawan Kapur, Krishna C. Saraswat R. Fabian W. Pease Dept. of Electrical Engineering, Stanford University, CA 94305 Acknowledgement : Office of Naval Research Award # N00014-01-1-0741. MARCO Interconnect Focus Center

2. 14 February, 2004SLIP, 2004 Interconnect Scaling Scaling Trends – More wires – Shrinking and more metal levels – Resistance & Capacitance   Performance deteriorates Metrics – Delay – Power dissipation – Cross talk (data reliability) – Bandwidth – Area – Reliability Mitigating Solutions (Technology)  Al to Cu  lower k: Two Methods From ITRS

3. 14 February, 2004SLIP, 2004 Dielectric Technology Non-homogeneous Homogeneous Metal Low-k SiO 2 Si Power: Homogeneous Cross talk: Non-homogeneous Delay: – local: C (homogeneous) – long distance: RC (Unclear?)

4. 14 February, 2004SLIP, 2004 Self-Consistent Temperature Distribution Fourier’s Law Electrical Resistance   [T] –Thermal Coefficient of Resistance –Barrier, Surface Scattering –Number of metal levels Thermal Resistance  1/k eff [T] –Number of metal levels –Via Effect Future ALDIPVDC-PVD Ignored Before

5. 14 February, 2004SLIP, 2004 Given Current Density, J. Find Temperature, T? Start with uniform T n [k] n – metal level k - iteration Copper Resistance Length demarcation Heating (q=J 2 rms  ) T n [k+1] T n [k] = T n [k+1] ? No: of metal levels, n Thermal Resistance, R th Stop Yes No Barrier effect Surface scattering Temperature Via Effect Rent’s Rule

6. 14 February, 2004SLIP, 2004 Electrical & Thermal Resistance Rent’s Rule –Wire Length Distribution RC Wire Delay –Local, Semi-global, Global Demarcation –Number of metal levels –Stack Height Thermal Resistance –Stack Height –Via Effect Gate Pitch I.D.F Local Semi - Global Efficient heat conductors (reduce thermal resistance)

7. 14 February, 2004SLIP, 2004 Number of Metal Levels Fluctuations are artifacts of numerical calculations Power, Ground & Clock lines not included

8. 14 February, 2004SLIP, 2004 Maximum Temperature Rise  T~ 10    T~ 3    T  J 2   R Th

9. 14 February, 2004SLIP, 2004 Effective Thermal Resistance R th,eff =  H i / K eff, i Wire thickness H ~ 4   K eff ~constant High Conductivity of SiO 2 K eff ~ 3.5   Poor Conductivity of Low-k R th,eff ~ 1.5   R th,eff ~ 3   Surprising decrease!

10. 14 February, 2004SLIP, 2004 Electrical Resistivity-Global Wires Consistent Solution is larger by up to 15% Technology node (nm)

11. 14 February, 2004SLIP, 2004 Electrical Resistivity-Semi-Global Wires Negligible difference Wire Temperature ~ Substrate T Smaller wire pitch  Larger via density Technology node (nm)

12. 14 February, 2004SLIP, 2004 Wire Capacitance 70% of C total = C IMD C total = C IMD +C ILD Capacitance 1.6    IMD ~ 2   IMD is Low-k for both cases

13. 14 February, 2004SLIP, 2004 Delay Metric - RC/L 2 Capacitance advantage of homogeneous is offset by the increased resistance Is that all? Reliability R/Length ~ 50   C/Length ~1.6  

14. 14 February, 2004SLIP, 2004 Can Current Density go on Increasing? Required Current –Integration density Allowed Current –Electromigration –IR drop in supply voltage Black’s Law If J  T   MTF 

15. 14 February, 2004SLIP, 2004 Mean Time to Failure Non-homogeneous is better. Reliability Cross-talk Larger Temperature  Lower MTF

16. 14 February, 2004SLIP, 2004 Is there a consistent solution? Black’s Law Joule Heating r - Duty Cycle

17. 14 February, 2004SLIP, 2004 Consistent Solution Joule Heating Black’s Law Point of intersection is the consistent solution

18. 14 February, 2004SLIP, 2004 Consistent Solution

19. 14 February, 2004SLIP, 2004 Conclusion Consistent Algorithm to estimate –Thermal Profiles –Electromigration constraints Comparison of Dielectric Technologies –Power, Delay - Homogeneous –Cross-talk, Reliability – Non-homogeneous

20. 14 February, 2004SLIP, 2004 Thank You

21. 14 February, 2004SLIP, 2004 Back Up

22. 14 February, 2004SLIP, 2004 Wire Length

23. 14 February, 2004SLIP, 2004 Electrical Resistivity - Local Wires Negligible difference Wire Temperature ~ Substrate T Smaller wire pitch  Larger via density

24. 14 February, 2004SLIP, 2004 Duty Cycle Higher Duty Cycle  More heating  J RMS should  to keep MTF same.

25. 14 February, 2004SLIP, 2004 SiO 2 - Low-k Comparison Red lines – SiO 2 Delay is larger