A T HERMAL -D RIVEN F LOORPLANNING A LGORITHM FOR 3D IC S Jason Cong, Jie Wei, and Yan Zhang ICCAD

OUTLINE Introduction Problem formulation 3D thermal-driven floorplanning algorithm Experimental results Conclusion 2

I NTRODUCTION 3 Motivation for 3D ICs Reduce interconnect delays Source: Proc of the IEEE, 2001

I NTRODUCTION 4 Different 3D technologies Chip level integration Block level integration (this paper focus) Cell level integration(over 500k) Chip level Block level Cell level

I NTRODUCTION The current thermal models: 1. Numerical computing methods such as FEM(Finite Element Method)[8] and FDM(Finite Difference Methods)[21][22] 2. Compact resistive network[20] 3. Simplified closed-form formula[6][14] Time-consuming :1>2>3 Accurate:1>2>3 5

P ROBLEM FORMULATION 6

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3D FLOORPLANNING ALGORITHM 2D floorplanning algorithm: sequence pair[18],BSG[16],B*-Tree[4],O- Tree[11],CBL[12],TCG[17],etc. 3D floorplanning algorithm[CBA(Combined Bucket and 2D Array)]: 2D floorplanning algorithm + a bucket structure 2D floorplanning(TCG[17]): is used to represent each layer A bucket structure: is posed on the circuit stack 8

3D FLOORPLANNING ALGORITHM TCG(Transitive Closure Graphs [DAC 2001]): two constraint graphs : horizontal and vertical graph. 9

3D FLOORPLANNING ALGORITHM A bucket structure: IB(i) : In each bucket i, indexes of the blocks that intersect with the bucket are stored. IBT(j) : each block j stores indexes to all the buckets that overlap with the block. 10 Die3 Die2 Die1

3D FLOORPLANNING ALGORITHM A bucket structure: 11 3DFP of a 2-layer 7-block floorplan

3D FLOORPLANNING ALGORITHM SA(Simulated Annealing): Cost = a*nwl+b*narea+c*nvc+d*C T Solution Perturbation: Rotation Swap Reverse Move Interlayer swap Z-neighbor swap Are based on the concept of z-axis neighbor Z-neighbor move Are based on the concept of z-axis neighbor 12

3D FLOORPLANNING ALGORITHM Z-axis neighbor: The definition is based on the bucket structure. The z-axis neighbor of a given block j. Zn(j):the block k in B(j) with the minimum neighboring cost zc(j,k)=a*|A k -A j |+b*dist(k,j) dist(k,j)=|x k -x j |+|y k -y j | Z-neighbor swap:is to swap a block with its z- axis neighbor. Z-neighbor move: B i is moved from its own layer l i to the layer l j where B j locates. B i is positioned adjacent to B j at either top or right side. 13

3D FLOORPLANNING ALGORITHM 14 After a z-neighbor swap operation on b and f After a z-neighbor move operation on d

3D FLOORPLANNING ALGORITHM Thermal model: Compact resistive thermal model[24] Simplified Closed-form thermal model Vertical Heat Flow Analysis Horizontal Heat Flow Analysis 15

3D FLOORPLANNING ALGORITHM 16 Vertical Heat Flow Analysis Considering only 1-D heat flow, minimize the Elmore delay like formula Horizontal Heat Flow Analysis Even out the temperature distribution on the chip, avoiding “hotspot”

E XPERIMENTAL RESULTS 17 With the new operations, 3D-FP can improve the area by 5% and wirelength by 3%

E XPERIMENTAL RESULTS 18 3D-FP-T can greatly reduce the temperature by 56% with 9.7x runtime

E XPERIMENTAL RESULTS 19 3D-FP-T-Fast can reduce the temperature by 40% with 1.8x runtime 3D-FP-T-Hybrid can reduce the temperature by 50% with 3.2x runtime

E XPERIMENTAL RESULTS 20 - by commercial FEM based tool (CFD-ACE+) - ami33 benchmark with 33 blocks and 4 layers