### 抜粋

Three-dimensional integrated circuits (3-D ICs), i.e., stacked dies, can alleviate the interconnect problem coming with the decreasing feature size and increasing integration density, and promise a solution to heterogenous integration. The vertical connection, which is generally implemented by the through-the-silicon via, is a key technology for 3-D ICs. In this paper, given 3-D circuit placement or floorplan results with white space reserved between blocks for inter-layer interconnections, we proposed methods for assigning inter-layer signal via locations. Introducing a grid structure on the chip, the inter-layer via assignment of twolayer chips can be optimally solved by a convex-cost max-flow formulation with signal via congestion optimized. As for 3-D ICs with three or more layers, the inter-layer signal via assignment is modeled as an integral mincost multi-commodity flow problem, which is solved by a heuristic method based on the lagrangian relaxation. Relaxing the capacity constraints in the grids, we transfer the min-cost multi-commodity flow problem to a sequence of lagrangian sub-problems, which are solved by finding a sequence of shortest paths. The complexity of solving a lagrangian sub-problem is O(n_{nt}n^{2}
_{g}), where n_{nt} is the number of nets and n_{g} is the number of grids on one chip layer. The experimental results demonstrated the effectiveness of the method.

元の言語 | English |
---|---|

ページ（範囲） | 1080-1087 |

ページ数 | 8 |

ジャーナル | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

巻 | E92-A |

発行部数 | 4 |

DOI | |

出版物ステータス | Published - 2009 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Signal Processing

## フィンガープリント Lagrangian relaxation based inter-layer signal via assignment for 3-D ICs' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E92-A*(4), 1080-1087. https://doi.org/10.1587/transfun.E92.A.1080