Redundant-Via-Aware ECO Routing

1. Redundant-Via-Aware ECO Routing Hsi-An Chien Ting-Chi Wang ASPDAC2014

2. Outline • INTRODUCTION • PROBLEM DEFINITION • THE PROPOSED APPROACH • EXPERIMENTAL RESULTS • CONCLUSIONS

3. INTRODUCTION • With the advent of the manufacturing strategy that requires redundant via insertion (RVI) for tackling single via failure to enhance the chip reliability and yield.

4. INTRODUCTION • Unfortunately, due to the large number of inserted redundant vias, a design could become too congested for engineering change order (ECO) routing to succeed.

5. INTRODUCTION

6. INTRODUCTION • By using a traditional ECO routing method, it is easy to get a feasible routing path that utilizes four vias, v6, v7, v8, and v9.

7. INTRODUCTION • But only redundant vias rv6 and rv8 can be inserted next to v6 and v8 while v7 and v9 become dead vias.

8. INTRODUCTION • If rv2 is removed, a shorter routing path that has two vias, v6 and v7, and one inserted redundant via rv6 for the ECO net can be found, as shown in Figure (c).

9. INTRODUCTION • To further reduce the amount of dead vias, we can replace rv1 and rv3 with rv’1 and rv’3,

10. PROBLEM DEFINITION • It’s a ECO routing problem where redundant vias are present in the given layout but can be considered for replacement or removal to increase the routability and improve the routing quality.

11. PROBLEM DEFINITION • The goal is to find a routing path with routing cost as small as possible. • The cost considers several routing factors, including wirelength, vias, dead vias.

12. THE PROPOSED APPROACH • For an easy presentation, each routing layer is virtually superimposed with a grid to form the 3D routing. • Each gridpointis a square on a metal layer, whose width is the minimum wire width on that layer.

13. THE PROPOSED APPROACH • To efficiently find the routing path to connect s and t, we exploit A* search.

14. THE PROPOSED APPROACH • Given a feasible gridpointg on Metal1 as shown in Figure (a).

15. THE PROPOSED APPROACH • Figure(b) shows the construction of the query region for g, which expands g by wsalong each side to form the query region qrg.

16. THE PROPOSED APPROACH • If the existing objects of Metal1 do not intersect with the query region , the gridpoint is feasible.

17. THE PROPOSED APPROACH • We can see that qrgoverlaps with qrrg1so it is not necessary to query the overlapped region between qrgand qrrg1 again.

18. THE PROPOSED APPROACH • The reduced query region rqrrg1 shown in Figure(d) is used to lower the search effort when examining whether rg1 is a feasible gridpoint.

19. THE PROPOSED APPROACH • the rqrtg1 intersects with an existing wire segment on the same layer , and therefore tg1 is not a feasible gridpoint

20. THE PROPOSED APPROACH • Since existing redundant vias can be replaced or removed, they will be ignored in any query region

21. THE PROPOSED APPROACH • It’s allowed to be replaced with rv1 (Figure (g)) or removed out of rqrrg2(Figure (h)), so rg2 is treated as a feasible neighboring gridpoint for rg1.

22. THE PROPOSED APPROACH • To check the upper neighboring gridpointugon Metal2 of the gridpointg. • We can also deal with different wire widths and spacings on adjacent layers.

23. THE PROPOSED APPROACH • We pick the nearest upper neighbor ugand locate the via connecting g and ugat the intersection point v

24. THE PROPOSED APPROACH • Our path finding A* search algorithm uses the following cost function: • g(n) : the actual routing cost from the source node s to the current node n • h(n) : the Manhattan distance between n and t.

25. THE PROPOSED APPROACH • g(n) is the cumulative cost of the best path p from s to n • g(n) = G(n) + αV (n) + βI(n) + γR(n)

26. THE PROPOSED APPROACH • G(n) =Pd +2*Nd • Pd: number of gridpoints along preferred routing directions • Nd: the number of gridpoints along non-preferred routing directions.

27. THE PROPOSED APPROACH • V (n): amount of viason the path p • I(n): total number of “illegal redundant via insertions”among these new • R(n): total number of “illegal redundant via replacements”

28. THE PROPOSED APPROACH • To enhance the efficiency, our algorithm will search a certain amount of consecutive gridpoints along a preferred routing direction as a whole. • and return the maximum number of consecutive feasible gridpoints

29. THE PROPOSED APPROACH • And return the maximum number of consecutive feasible gridpoints.

30. EXPERIMENTAL RESULTS • All experiments were conducted on a Linux workstation with an 2.2 GHz AMD CPU and 8G memory.

31. EXPERIMENTAL RESULTS

32. CONCLUSIONS • An ECO routing approach that considers redundant via replacement, removal, and insertion. • Successfully increased the routing completion rate and improved the routing quality.