Interconnect delay model in dsm technology

1. CROSSTALK AWARE BANDWIDTH
MODELLING FOR VLSI RC GLOBAL
INTERCONNECTS USING 2-Π MODEL
Presented By
Santosh Kumar Chhotray
National Institute of Technology, Durgapur

2. CONTENTS
 Introduction
 Crosstalk noise
 Crosstalk noise effects
 Crosstalk noise model
 Proposed estimation method
 Result
 References
 Conclusion

3. INTRODUCTION
 DSM Technology

4. CROSSTALK NOISE
-Unwanted coupling voltages
-No. of metal layers
-Density of integration
-Reduction of spacing between lines

5. CROSSTALK NOISE EFFECTS
-Noise on non-switching wires
-Increased delay on switching
wires
-Limited bandwidth

6. CROSSTALK NOISE MODEL
Two partially coupled interconnects

7. PROPOSED ESTIMATION METHOD
 Aggressor Waveform
0
( )
dd a
aagg
dd a
t
V t
V t
V t




 
 
 
2
1
( )agg dd
a
V s V
s 

In S-domain
In Elmore delay model, the delay time between node na1 and
node na2, D1→2 is represented as
   1 2 1 1 2 3 2 2 3a a a c a a a c aD R C C C C R C C C       

8. CONT..
 Aggressor Waveform
Where
Now becomes
   1 1 2 3 2 2 3a a a a c a a a c aR C C C C R C C C       
Effective capacitance
   1 1 2 3 2 2 3a a a c a a a c aT R C C C C R C C C      
3 3dj a aT R C
   1 1 2 3 2 2 3a a a a c a eff a a c a effR C C C C R C C C       
a
3 3 1 dj
T
T
a eff aC C e

 
  
 

9. PROPOSED ESTIMATION METHOD
 Analytic Waveform of Victim Interconnect
 1 2 1 1 2
3 2
( ) ( )
1
v v v v v c
noise agg
R R C s R R C s
V s V s
as bs ds
 

  
 1 2 3 1 1 3v v v v v c va R R R C C C C 
    1 1 2 2 3 3 3 3 3 2 1 2v v v v C v v v v v v c v vb R C R C C C R C R C C C R R        
   1 1 2 3 2 2 3 3 3v v v c v v v c v v vd R C C C C R C C C R C       

10. CONT..
Now Vnoise(S) can be written as
where poles s1, s2 and s3 are roots are of . When
relationship of s1< s2<< s3 is satisfied, the most
dominant pole s3 is represented as 1/d. Replacing d by
Vnoise (S) obtained as
31 2
1 2 3
( ) ( )noise agg
KK K
V s V s
s s s s s s
 
   
   
v
 
 
1 2
( )
1
v v c
noise dd
v a
R R C
V s V
s s 




11. CONT..
After solving with partial fraction
Now taking ILT
 1 2 1
( )
1
v v v
noise c dd
a v
R R
V s C V
s s

 
  
  
 
 1 2
( ) 1 v
t
tv v
noise c dd
a
R R
V t C V e


 
  
  

12. DELAY ESTIMATION
Simplifying above equation
 1 2
0.5 1 v
t
tv v
dd c dd
a
R R
V C V e


 
  
  
50%
1 2
1
(1/ )
2
v a
c
v v
t C
R R
 


For delay estimation equating
Vnoise(S)=0.5 Vdd

13. BANDWIDTH ESTIMATION
Rearranging above equation
Now replacing S by
 
 
1 2( )
( )
( ) 1
v vnoise
c
agg v a
R RV s
H s sC
V s s 

 

 
 
1 2
( )
1
v v
c
a v
R R s
H s C
s 
 
  
 
  
 
1 2
2 2
( )
1
c v v v
a v
C R R j
H j
 

  
 


j

14. CONT..
Now to get 3db bandwidth
 
 
1 2
2 2
1
2 1
c v v
v v
C R R 
  
 
  
  
 
   
3 2 22
1 22 2
a
dB
c v v a v
f
C R R

  
 
 

15. RESULTS
Bandwidth for different value of R

16. CONT..
50% delay for different value of Rs

17. CONT..

18. CONCLUSION
For delay estimation
For bandwidth estimation
   
3 2 22
1 22 2
a
dB
c v v a v
f
C R R

  
 
 
50%
1 2
1
(1/ )
2
v a
c
v v
t C
R R
 



19. REFERENCES
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20. CONT..
 [8] Kar R., Maheshwari V., Maqbool Mohd., Mal A. K., Bhattacharjee
A. K., 2010 , “A Closed form Delay Evaluation Approach using Burr’s
Distribution Function for High Speed On-Chip RC Interconnects”,
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21. THANK YOU