Self-Consistent Power/Performance/Reliability Analysis for Copper Interconnects

1. 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 SLIP, 2004

2. 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 SLIP, 2004

3. Metal SiO2 Low-k Si Homogeneous Non-homogeneous Dielectric Technology • Power:Homogeneous • Cross talk:Non-homogeneous • Delay: • local: C (homogeneous) • long distance: RC (Unclear?) SLIP, 2004

4. Ignored Before Future ALD IPVD C-PVD Self-Consistent Temperature Distribution • Fourier’s Law • Electrical Resistance  [T] • Thermal Coefficient of Resistance • Barrier, Surface Scattering • Number of metal levels • Thermal Resistance  1/keff[T] • Number of metal levels • Via Effect SLIP, 2004

5. Start with uniform Tn[k] Barrier effect Surface scattering Temperature Copper Resistance Rent’s Rule Length demarcation Heating (q=J2rms ) No: of metal levels, n Via Effect Thermal Resistance, Rth No Tn[k] = Tn[k+1] ? Tn[k+1] Yes n – metal level k - iteration Stop GivenCurrent Density, J.FindTemperature, T? SLIP, 2004

6. I.D.F Semi - Global Local Global Efficient heat conductors (reduce thermal resistance) 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 SLIP, 2004

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

8. Maximum Temperature Rise T  J2RTh T~ 10  T~ 3  SLIP, 2004

9. Effective Thermal Resistance Rth,eff=Hi / Keff, i Surprising decrease! Wire thickness H ~ 4  Rth,eff ~ 1.5  Keff ~ 3.5  Poor Conductivity of Low-k Rth,eff ~ 3  Keff ~constant High Conductivity of SiO2 SLIP, 2004

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

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

12. Wire Capacitance Ctotal= CIMD+CILD 70% of Ctotal = CIMD IMD is Low-k for both cases Capacitance 1.6  IMD ~ 2  SLIP, 2004

13. Delay Metric - RC/L2 R/Length ~ 50  C/Length ~1.6  Capacitance advantage of homogeneous is offset by the increased resistance Is that all? Reliability SLIP, 2004

14. 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 SLIP, 2004

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

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

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

18. Consistent Solution SLIP, 2004

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

20. Thank You SLIP, 2004

21. Back Up SLIP, 2004

22. Wire Length SLIP, 2004

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

24. Duty Cycle • Higher Duty Cycle •  More heating • JRMS should  to keep MTF same. SLIP, 2004

25. SiO2 - Low-k Comparison Red lines – SiO2 Delay is larger SLIP, 2004