1. Authors: Jia-Wei Fang,Chin-Hsiung Hsu,and Yao-Wen Chang DAC 2007 speaker: sheng yi An Integer Linear Programming Based Routing Algorithm for Flip-Chip Design

2. Outline 2 Introduction Problem formulation RDL routing algorithm Experimental results Conclusions

3. Introduction 3 The increasing complexity and decreasing feature size of VLSI designs make the demand of more I/O pads a significant problem to package technologies. An advanced packaging technology, the flip-chip (FC) package[Fig.1.(a)] is created for higher integration density and larger I/O counts. However, in recent IC designs, the I/O pads are still placed along the boundary of a die. This placement does not suit for the flip-chip package well. As a result, the top metal or an extra metal layer, called a Re-Distribution Layer (RDL)[Fig.1.(b)] is used to redistribute the wire-bonding pads to the bump pads without changing the placement of the I/O pads

4. Introduction 4

5. 5 There are two kinds of the RDL routing problems for flip-chip design. 1.free-assignment routing :a router has the freedom to assign a wire-bonding pad to bump pads during routing. 2.pre-assignment routing :the mapping among wire-bonding pads and bump pads are defined before routing and can not be changed. ps: pre-assignment problem is more popular in practice since the functions of wire-bonding and bump pads are typically pre-defined by IC and packaging designers.

6. Problem formulation 6

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11. Problem formulation 11 Problem 1 :The single-layer pre-assignment routing problem in the flip-chip design is to connect a set P of wire-bonding pads and a set B of bump pads according to pre- defined netlist with wire width and signal skew constrains so that no wire crosses each other, no signal skew constrain is violated, and the total wirelength is minimized under the 100% routability guarantee.

12. RDL routing algorithm 12 Algorithm overview

13. RDL routing algorithm 13 Notations and construct the routing network G: [global routing : ILP Formulation]

14. RDL routing algorithm 14 Notations: E: a set of edges which are the candidate segments of the global routing paths of nets. There are four types of edges: 1.the directed edge from a wire-bonding pad to a bump pad. 2.the directed edge from a wire-bonding pad to an ILP node. 3.the directed edge from an ILP node to a bump pad. 4.the directed edge from an ILP node to another ILP node. [global routing : ILP Formulation]

15. RDL routing algorithm 15 [global routing : ILP Formulation]

16. RDL routing algorithm 16 [global routing : ILP Formulation]

17. RDL routing algorithm 17 [global routing : ILP Formulation]

18. RDL routing algorithm 18 [global routing : ILP Formulation]

19. RDL routing algorithm 19 [global routing : ILP Formulation]

20. RDL routing algorithm 20 [global routing : ILP Formulation]

21. RDL routing algorithm Constraint (1): avoids the crossing Constraint (2): is used to avoid the congestion overflow of a tile. Constraint (3): avoids the congestion overflow of an interval between two pads.(for the edges passing through the same interval.) Constraint (4): formulates the signal-skew constraint between two nets. Constraint (5): guarantees that at least one edge of the wire- bonding pad p i of net n i be chosen. Constraint (6): flow conservation. 21 [global routing : ILP Formulation]

22. RDL routing algorithm Two ILP reduction techniques to reduce the size of network G and the number of variables and constraints in the ILP: (1).Constraint Graph Based Pruning (2).ILP Node Merging 22 [global routing:ILP reduction]

23. RDL routing algorithm 23 [ 出處 :2006 IEEE Monotonic Parallel and Orthogonal Routing for single-layer Ball Grid Array Package] A single netlist is monotonic if and only if nets on each row are in increasing order.

24. RDL routing algorithm (1).Constraint Graph Based Pruning: 24 [global routing:ILP reduction]

25. RDL routing algorithm 25 [global routing:ILP reduction]

26. RDL routing algorithm 26 [global routing:ILP reduction]

27. RDL routing algorithm 27 [global routing:ILP reduction]

28. RDL routing algorithm 28 [global routing:Non-monotonic]

29. RDL routing algorithm Passing point assignment :passing points are transformed from ILP nodes in order to distribute nets pass through the same interval, according to their wire widths and further signal-skew constraints. Net-Ordering Determination 29 [Detail routing:passing point and Net-order Determination]

30. RDL routing algorithm 30 [Detail routing:X-based Gridless Routing]

31. Experimental results 31 #Nets: the number of nets #Skew pairs: the number of matched nets with skew constrains #Wire widths: the number of variable wire widths #Rp: the number of wire-bonding rings #p: the number of the wire-bonding pad #Rb: the number of bump pad rings #b: the number of bump pads

32. Experimental results 32 Imp. Of CG(%):the reduction rate of the variables by using constrain graph pruning. Imp. Of NM(%):the reduction rate over the results listed in the Column “Imp. Of CG(%)” by using the ILP node merging. Total: the final resulting number of variables (constraints)

33. Experimental results 33

34. Conclusions 34 The first algorithm for the pre-assignment RDL routing problem, consider signal skews variable wire widths, U-turn routes, and total wirelength minimization.