RWCap: A Floating Random Walk Solver for 3-D Capacitance Extraction of Very-Large-Scale Integration Interconnects

摘要

A floating random walk (FRW) solver, called RWCap, is presented for the capacitance extraction of very-large-scale integration (VLSI) interconnects. An approach, including the numerical characterization of the cross-interface transition probability and weight value, is proposed to accelerate the extraction of structures with multiple dielectric layers. A comprehensive variance reduction scheme based on the importance sampling and stratified sampling is proposed to improve the convergence rate of the FRW algorithm. Finally, the space management technique using an octree data structure and the parallel computing technique are presented to further improve the efficiency. Numerical experiments are carried out with the test cases generated under the 180 and 45-nm process technologies. They demonstrate that the proposed multidielectric FRW algorithm achieves up to $160times$ speedup over the FRW algorithm using spherical transition domains to cross dielectric interface, with very small memory overhead. The variance reduction techniques further bring $3times$ or more speedup without memory overhead and the loss of accuracy. The RWCap also outperforms other existing FRW algorithm and fast boundary element method solvers in terms of computational time or scalability. The experiments on an 8-core CPU machine show that the parallel RWCap is over $6times$ faster than its serial-computing version.