THEORETICAL LIMITS FOR SIGNAL REFLECTIONS DUE TO INDUCTANCE FOR ON-CHIP INTERCONNECTIONS

1. THEORETICAL LIMITS FOR SIGNAL REFLECTIONS DUE TO INDUCTANCE FOR ON-CHIP INTERCONNECTIONS F. Huret, E. Paleczny, P. Kennis Institut d ’Electronique et de Microélectronique du Nord, UMR CNRS 9929 D. Deschacht, G. Servel Laboratoire d’Informatique, de Robotique et de Microélectronique, UMR CNRS 5506. SLIP ’2000, San Diego, April 8-9th.

2. OUTLINE OF THE TALK Introduction Theoretical limits Electromagnetic analysis : - Methodology - Application Limits between RLC and RC models Illustration of the theoretical limits : - in frequency-domain - in time domain Comparison with previous work Conclusion

3. INTRODUCTION 10 years of evolution 1989 1999 • 0.7µm, 2 metal layers • Up to 100,000 devices on a chip • Typical CPU frequency 50MHz • 0.25µm, 6 metal • Up to 10,000,000 devices on a chip • Typical CPU frequency 400 MHz IC

4. INTRODUCTION With the continued scaling down of technology, increased die aera : * cross-section decreases * interconnect length increases interconnections : blocking point of performances improvement Introduction of new materials such as Cu inclusion of inductance ?

5. INTRODUCTION Interconnect delay dominates gate delay in current deep submicronic VLSI circuits. More accurate interconnect models and signal propagation characterization are required. With faster on-chip rise times inductance is becoming more important. Electromagnetic analysis is needed.

6. THEORETICAL LIMITS Short lines : Static hypothesis Long lines : Traveling wave

7. THEORETICAL LIMITS Range of lengths for inductance inclusion : We have to determine a : attenuation factor b : phase factor x : attenuation coefficient

8. ELECTROMAGNETIC ANALYSIS Methodology INTERCONNECTION = WAVEGUIDE a Attenuation factor dB/cm ou Np/cm Full wave analysis Finite Element Method b Phase factor rad/cm Zc Characteristic impedance Propagation parameters of the waveguide

9. ELECTROMAGNETIC ANALYSIS Methodology Definitons of the voltage-current matrices used in this analysis

10. ELECTROMAGNETIC ANALYSIS Methodology Vout(t) Vin(t) a(freq) b(freq) Zc(freq) + Matched Load Impedances F.F.T. F.F.T.-1 Chain Matrix Vin(freq) Vout(freq) * F.F.T = Fast Fourier Transform

11. 0.8 mm M5 0.8 mm ELECTROMAGNETIC ANALYSIS Application Interconnection geometry and environment passivation passivation 2.4 mm 2.4 mm M5 SiO2 M5 SiO2 7.3 mm 7.3 mm 500 mm Si bulk 7Wcm 1st configuration 2nd configuration 3rd configuration Metal 5 : W=1 mm T= 1 mm Aluminium or Copper

12. ELECTROMAGNETIC ANALYSIS Application Frequency behavior of the attenuation factors

13. ELECTROMAGNETIC ANALYSIS Application Frequency behavior of the phase factors

14. ELECTROMAGNETIC ANALYSIS Application Attenuation determination Traveling wave Attenuation value of the wave, for 10 GHz, versus interconnection length

15. ELECTROMAGNETIC ANALYSIS Application Theoretical limits : We have determined a, b To determine x : comparison output signal between RC and RLCG models

16. OUTLINE OF THE TALK Introduction Theoretical limits Electromagnetic analysis : - Methodology - Application Limits between RLC and RC models Illustration of the theoretical limits : - in frequency-domain - in time domain Conclusion

17. LIMIT BETWEEN RLC AND RC MODELS The RLCG line model deduced from the electromagnetic analysis :

18. LIMIT BETWEEN RLC AND RC MODELS These calculated values are used to build the distributed p RC model n cells COMPARISON BETWEEN : HSPICE simulations : RC model Electromagnetic analysis : RLC model

19. LIMIT BETWEEN RLC AND RC MODELS Waveform of input and output signals in the range of lengths with inductance effect

20. LIMIT BETWEEN RLC AND RC MODELS Waveform of input and output signals in the range of lengths with inductance effect

21. LIMIT BETWEEN RLC AND RC MODELS Attenuation determination : Limit : the amplitude of the reflected wave is sufficiently low to give the reflection effect negligible

22. OUTLINE OF THE TALK Theoretical limits : We have determined a, b, x Illustration of the theoretical limits : - in frequency-domain - in time domain

23. ILLUSTRATION OF THEORETICAL LIMITS in the frequency-domain

24. ILLUSTRATION OF THEORETICAL LIMITS in the frequency-domain Frequency Time domain

25. ILLUSTRATION OF THEORETICAL LIMITS in the time-domain

26. OUTLINE OF THE TALK Introduction Theoretical limits Electromagnetic analysis : - Methodology - Application Limits between RLC and RC models Illustration of the theoretical limits : - in frequency-domain - in time domain Comparison with previous work Conclusion

27. COMPARISON WITH PREVIOUS WORK « Figures of Merit to characterize the Importance of On-chip Inductance » DAC 98, June 1998  The two figures of merit can be combined into a two sided inequality that determines the range of the length of interconnect in which inductance effects are significant : 1st configuration : R = 17300 W/m C = 170 pF/m L = 490 nH/m G # 0 2nd configuration : R = 17300 W/m C = 63.6 pF/m L = 655 nH/m G # 0

28. COMPARISON WITH PREVIOUS WORK

29. COMPARISON WITH PREVIOUS WORK

30. CONCLUSION A full-wave electromagnetic analysis have been presented to build accurate interconnect models, including inductance effects. New limits for signal reflections due to inductance for on-chip interconnections have been proposed.

31. CONCLUSION These limits have been illustrated with typical interconnection geometries, for Al and Cu wires. This study shows evidence demonstrating that a range exists for which inductance effects cannot be neglected and requires a transmission line model.

32. CONCLUSION FUTURE WORK : Interconnect coupling : taking into account not only the coupling capacitance, but also the impact of inductance and mutual inductance.