1. Hsi-An Chien Ting-Chi Wang Redundant-Via-Aware ECO Routing 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 If we are allowed to perturb a given layout a bit by properly replacing or removing existing redundant vias without changing the original routing connectivity, we are able to increase the routability and improve the routing quality for ECO routing.

6. INTRODUCTION

7. However, without disturbing the original design, we cannot obtain a feasible routing path for the ECO net. Now if we perturb the original layout a bit by allowing existing redundant vias to be considered for replacement or removal, a routing path without violating design rules can be found for the ECO net

8. INTRODUCTION The redundant via rv 1 is replaced with rv 1 ’ The redundant via rv 2 is removed, making v 2 (highlighted by a dash circle) become a dead via. This example shows that a minor perturbation to existing redundant vias enables us to cope with the routing failure and thus to increase the routability.

9. INTRODUCTION By using a traditional ECO routing method, it is easy to get a feasible routing path that utilizes four vias, v 6, v 7, v 8, and v 9.

10. INTRODUCTION But only redundant vias rv 6 and rv 8 can be inserted next to v 6 and v 8 while v 7 and v 9 become dead vias.

11. INTRODUCTION But only redundant vias rv 6 and rv 8 can be inserted next to v 6 and v 8 while v 7 and v 9 become dead vias.

12. INTRODUCTION If rv 2 is removed, a shorter routing path that has two vias, v 6 and v 7, and one inserted redundant via rv 6 for the ECO net can be found, as shown in Figure (c).

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

14. INTRODUCTION This example shows that by allowing existing redundant vias to be replaced or removed, we could enhance the routing quality.

15. 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.

16. 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.

17. PROBLEM DEFINITION The ECO routing problem we consider is to find a path p that connects the source pin and target pin of a 2-pin ECO net with space reserved for subsequent redundant via insertion/replacement.

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

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

20. THE PROPOSED APPROACH Given a feasible gridpoint g on Metal1 as shown in Figure (a).

21. THE PROPOSED APPROACH Figure(b) shows the construction of the query region for g, which expands g by ws along each side to form the query region qr g.

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

23. THE PROPOSED APPROACH We can see that q rg overlaps with qr rg 1 so it is not necessary to query the overlapped region between qr g and qr rg 1 again.

24. THE PROPOSED APPROACH The reduced query region rqr rg 1 shown in Figure(d) is used to lower the search effort when examining whether rg 1 is a feasible gridpoint.

25. THE PROPOSED APPROACH the rqr tg 1 intersects with an existing wire segment on the same layer, and therefore tg 1 is not a feasible gridpoint

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

27. THE PROPOSED APPROACH It’s allowed to be replaced with rv 1 (Figure (g)) or removed out of rqr rg 2 (Figure (h)), so rg 2 is treated as a feasible neighboring gridpoint for rg 1.

28. THE PROPOSED APPROACH To check the upper neighboring gridpoint ug on Metal2 of the gridpoint g. We can also deal with different wire widths and spacings on adjacent layers.

29. THE PROPOSED APPROACH We pick the nearest upper neighbor ug and locate the via connecting g and ug at the intersection point v

30. 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.

31. 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)

32. 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.

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

34. 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

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

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

37. EXPERIMENTAL RESULTS

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