THEORETICAL LIMITS FOR SIGNAL REFLECTIONS DUE TO INDUCTANCE FOR ON-CHIP INTERCONNECTIONS F. Huret, E. Paleczny, P. Kennis F. Huret, E. Paleczny, P. Kennis Institut d ’Electronique et de Microélectronique du Nord, UMR CNRS 9929 D. Deschacht, G. Servel D. Deschacht, G. Servel Laboratoire d’Informatique, de Robotique Laboratoire d’Informatique, de Robotique et de Microélectronique, UMR CNRS et de Microélectronique, UMR CNRS SLIP ’2000, San Diego, April 8-9th. SLIP ’2000, San Diego, April 8-9th.
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
INTRODUCTION 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 10 years of evolution evolution
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 ?
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.
THEORETICAL LIMITS L ong lines : Static hypothesis Short lines : Traveling wave
Range of lengths for inductance inclusion : We have to determine attenuation factor phase factor x : attenuation coefficient THEORETICAL LIMITS
Propagation parameters of the waveguide INTERCONNECTION = WAVEGUIDE Phase factor rad/cm Attenuation factor dB/cm ou Np/cm Zc Characteristic impedance ELECTROMAGNETIC ANALYSIS Methodology Full wave analysis Finite Element Method
ELECTROMAGNETIC ANALYSIS Methodology Definitons of the voltage-current matrices used in this analysis
ELECTROMAGNETIC ANALYSIS Methodology Vin(t) Vout(t) Vin(freq) (freq) (freq) Zc(freq) Matched Load Impedances Chain Matrix Vout(freq) F.F.T * F.F.T = Fast Fourier Transform F.F.T.
ELECTROMAGNETIC ANALYSIS Application Interconnection geometry and environment 0.8 m M5 0.8 m 2.4 m M5 7.3 m passivation SiO2 Si bulk 7 cm 500 m 2.4 m M5 7.3 m passivation SiO2 2 nd configuration 1 st configuration 3 rd configuration Metal 5 : W=1 m T= 1 m Aluminium or Copper
ELECTROMAGNETIC ANALYSIS Application Frequency behavior of the attenuation factors
ELECTROMAGNETIC ANALYSIS Application Frequency behavior of the phase factors
ELECTROMAGNETIC ANALYSIS Application Attenuation determination Traveling wave Attenuation value of the wave, for 10 GHz, versus interconnection length
Theoretical limits : We have determined To determine x : comparison output signal between RC and RLCG models ELECTROMAGNETIC ANALYSIS Application
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
LIMIT BETWEEN RLC AND RC MODELS The RLCG line model deduced from the electromagnetic analysis :
These calculated values are used to build the distributed RC model LIMIT BETWEEN RLC AND RC MODELS n cells COMPARISON BETWEEN : HSPICE simulations : RC model Electromagnetic analysis : RLC model
LIMIT BETWEEN RLC AND RC MODELS Waveform of input and output signals in the range of lengths with inductance effect
LIMIT BETWEEN RLC AND RC MODELS Waveform of input and output signals in the range of lengths with inductance effect
LIMIT BETWEEN RLC AND RC MODELS Attenuation determination : Limit : the amplitude of the reflected wave is sufficiently low to give the reflection effect negligible
OUTLINE OF THE TALK Illustration of the theoretical limits : - in frequency-domain - in time domain Theoretical limits : We have determined x
ILLUSTRATION OF THEORETICAL LIMITS in the frequency-domain
Frequency Time domain ILLUSTRATION OF THEORETICAL LIMITS in the frequency-domain
ILLUSTRATION OF THEORETICAL LIMITS in the time-domain
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
COMPARISON WITH PREVIOUS WORK 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 : « Figures of Merit to characterize the Importance of On-chip Inductance » DAC 98, June st configuration : R = /m C = 170 pF/m L = 490 nH/m G # 0 2 nd configuration : R = /m C = 63.6 pF/m L = 655 nH/m G # 0
COMPARISON WITH PREVIOUS WORK
COMPARISON WITH PREVIOUS WORK
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.
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.
CONCLUSION FUTURE WORK : Interconnect coupling : taking into account not only the coupling capacitance, but also the impact of inductance and mutual inductance.