Fast floating random walk algorithm formulti-dielectric capacitance extraction with numerical characterization of Green´s functions

The floating random walk (FRW) algorithm has several advantages for extracting 3D interconnect capacitance. However, for multi-layer dielectrics in VLSI technology, the efficiency of FRW algorithm would be degraded due to frequent stop of walks at dielectric interface and constraint of first-hop length especially in thin dielectrics. In this paper, we tackle these problems with the numerical characterization of Green´s function for cross-interface transition probabilities and the corresponding weight value. We also present a space management technique with Octree data structure to reduce the time of each hop and parallelize the whole FRW by multi-threaded programming. Numerical results show large speedup brought by the proposed techniques for structures under the VLSI technology with thin dielectric layers.