Capacitance extraction in lossy layered substrates via Barnes-Hut accelerated utilizing per-layer center-of-charge (CoC)

The Barnes-Hut (BH) algorithm hierarchically replaces groups of charges in lossless or lossy media with their respective centers-of-charge to enable evaluation of the electrostatic potential due to N charges in O(N log N) instead of O(N
²
) operations. In this paper we utilize per-layer CoC from all the layers spanned by the box for BH algorithm inorder to maintain the O(1/R
³
) field approximation accuracy and allows its generalization for rapid extraction of capacitance and conductance matrices in complex 3D interconnects embedded in lossy substrates. The accuracy of extraction is compared against Ansoft's Q3D results for the nets of IBM Plasma package.