Volume Reduction and Fast Generation of the Precharacterization Data for Floating Random Walk-Based Capacitance Extraction

Abstract

Precharacterizing the transition cubes containing stratified dielectrics is inevitable for the floating random walk (FRW)-based capacitance extraction. Each multilayer-dielectric transition cube is characterized by a pair of Green’s function table (GFT) and weight value table (WVT), and all these GFTs and WVTs usually have large volume and constitute the major memory cost of the FRW algorithm. In this work, we explore the geometric symmetry of the multilayer-dielectric transition cube to enable volume reduction and fast generation of the GFT and WVT. For a general transition cube with stratified dielectrics and the one with four equal-thickness dielectrics, two schemes are proposed to reduce the volume of GFT and WVT by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8\times $ </tex-math></inline-formula> and over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10\times $ </tex-math></inline-formula> , respectively. Accordingly, an approach for fast generation of the reduced GFT/WVT is proposed, which is proved to produce the same result as the original GFT/WVT values. And, an improved FRW algorithm is proposed to utilize the reduced GFTs/WVTs without the sacrifice of runtime or accuracy. Both theoretical analysis and numerical experiments are conducted to demonstrate the remarkable volume reduction of precharacterization data (GFTs/WVTs). The fast GFT/WVT generation approach and the improved FRW algorithm are also validated with numerical experiments, showing over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10\times $ </tex-math></inline-formula> speedup of the precharacterization process, and accurate and memory-efficient capacitance extraction as well.