1. 1 Interconnect and Packaging Lecture 8: Clock Meshes and Shunts Chung-Kuan Cheng UC San Diego

2. 2 I. Clock Meshes In Engineering practice, very deep balanced buffer tree + mesh is widely adopted for global clock distribution IBM Power 4: 64 by 64 grid at the bottom of an H- tree Intel IA: clock stripe at the bottom of a buffer tree. “ Skew Averaging ” : shunt at different levels “ Skew Averaging Factor ” determined by simulation. No guideline for routing resource planning known yet

3. 3 I. Clock Mesh Example (1) DEC Alpha 21264

4. 4 I. Clock Mesh Example (2) IBM Power4 H-tree drives one domain clock mesh 8x8 area buffers

5. 5 I. Clock Mesh Example (3) Intel Pentium 4 Tree drives three spines

6. 6 II. Multi-level mesh structure

7. 7 II. Linear Variations Model Process variation model Transistor length Wire width Linear variation model Power variation model Supply voltage varies randomly (10%)

8. 8 II. Simplified Circuit Model

9. 9 II. Transient Response when t<T V S1 =u(t) V s2 =0 Let Then V 1 = A + B V 2 = A - B

10. 10 II. Transient Response when t>T Let : then

11. 11 II. Skew Expression Assumptions: 1.T<<R s C 2.R s /R <<R s C/T Using first order Taylor expansion e x =1+x,

12. 12 II. Spice Validation of Skew Function

13. 13 II. Skew on mesh Conjectured skew expression Using regression to get k

14. 14 II. K values for n by n meshes

15. 15 II. Optimization Skew function Multi level skew function

16. 16 Die size 1cm by 1cm 100nm copper technology Ground Shielded Differential Signal Wires for Global Clock Distribution Routing area is normalized to the area of a 16 by 16 mesh with minimal wire width III. Experimental Settings +- GND

17. 17 III. Experimental Results Optimized wire width

18. 18 III. Optimal Routing Resources Allocation

19. 19 III. Skew reduction V.S. Mesh Area

20. 20 III. Experiments — Optimized Skew

21. 21 III. Delay Surfaces

22. 22 III. Robustness Against Supply Voltage Variations

23. 23 III. Inductance Considerations Delay error between RC and RLC will not exceed 15 % under following conditions: C L >> C R/Z 0 > 2 R 1 > nZ 0 (n is between 0.5 and 1.0) (In our network, working at 4G, Z 0 =339ohm R 1 =367ohm, R=5130ohm, C l =149.4fF, and C=14.3fF)

24. 24 IV. Simulation Results with inductance Without LWith L Spice simulation results at 4GHz

25. 25 IV. Inductance Diminishes Shunt Effects f(GHz)0.511.5233.545 skew(ps)3.94.25.87.59.9131726 0.5um wide 1.2 cm long copper wire Input skew 20ps