Quadratic placement for 3d circuits using z-cell shifting, 3d iterative refinement and simulated annealing

  • Authors:
  • Renato Hentschke;Guilherme Flach;Felipe Pinto;Ricardo Reis

  • Affiliations:
  • Universidade Federal do Rio Grande do Sul, Porto Alegre - RS - Brazil;Universidade Federal do Rio Grande do Sul, Porto Alegre - RS - Brazil;Universidade Federal do Rio Grande do Sul, Porto Alegre - RS - Brazil;Universidade Federal do Rio Grande do Sul, Porto Alegre - RS - Brazil

  • Venue:
  • SBCCI '06 Proceedings of the 19th annual symposium on Integrated circuits and systems design
  • Year:
  • 2006

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Abstract

This paper presents a quadratic placement algorithm to be applied for 3D circuits. We formulate the 3D problem to control the area balance and the number of 3D-Vias between tiers. We introduce the z-Cell Shifting operation in order to control the area balance. We also define a new operation for the refinement of the solution called 3D Iterative Refinement, that has a control statement to avoid excessive number of 3D-Vias in order to keep the feasibility of our placement solution. After quadratic placement, we move to the placement legalization that is based on min-cost max flow and Simulated Annealing. For detailed placement refinement, we apply Simulated Annealing without cell migration between tiers. Experimental results show that our placement flow targeting one tier is comparable to academic tools such as FastPlace, Capo and Dragon in wire length and running time when targeting a single tier. On multiple tiers, we can reduce the average wire length from 7% (2 tiers) to 32% (5 tiers) and worst wire length by 26% (2 tiers) to 52% (5 tiers). The number of 3D-Vias obtained is feasible since the area overhead introduced is always below 10%.