Improved pre‐characterization method for the random walk based capacitance extraction of multi‐dielectric VLSI interconnects

Abstract

Accurately extracting capacitances among the interconnects in modern multi-dielectric technology of integrated circuits is a challenging task. The floating random walk (FRW) algorithm is advantageous for capacitance extraction and has been extended by W. Yu et al. to accurately handle multi-dielectric structures with a precharacterization approach. In this paper, we improve this pre-characterization approach by permitting the cubic transition domains with three or four-dielectric layers. The techniques of pre-characterizing and utilizing these multi-dielectric transition cubes are proposed. Experiments on the test cases under actual manufacture technologies show that the proposed method brings 13× speedup on average, with affordable memory overhead. The experiments also validate the accuracy of the proposed method and reveal the significant error caused by the dielectric homogenization approach in a commercial FRW solver. Finally, on a machine with 12-core CPU, the parallel FRW algorithm equipped with the proposed pre-characterization method demonstrates more than 10× speedup of parallelization.

Accelerated Generation of Multi-Dielectric Green’s Function Table

“…学术界也研发了基于悬浮随 机行走的电容提取软件 RWCap [3,5] . 为将其扩展到 大规模复杂结构 [6][7][8][9][10] , 提高其并行处理能力 [11][12][13] , 相关学者也进行了大量的研究.…”

“…其次 是方差削减技术 [6] , 它可以让蒙特•卡罗法在更少 的随机行走数下收敛. 最后是预刻画技术 [7] , 它采 用有限差分, 为悬浮随机行走过程预备跳转使用 的采样概率表(格林函数表). 其中, 跨多层的多介 质格林函数表使悬浮随机行走过程中转移立方体 区域显著扩大, 大大降低随机行走的跳转次数, 加 速求解过程 [7] .…”

“…最后是预刻画技术 [7] , 它采 用有限差分, 为悬浮随机行走过程预备跳转使用 的采样概率表(格林函数表). 其中, 跨多层的多介 质格林函数表使悬浮随机行走过程中转移立方体 区域显著扩大, 大大降低随机行走的跳转次数, 加 速求解过程 [7] . 但是多介质格林函数表的生成需要 考虑介质交界面的所有可能的分布情况 [3,7] , 表的 建立过程耗时较长.…”