Effect of Multilayered Substrate on the Barnes-Hut Center-Of-Charge Clustering Approximation: Half-Space Case Study

The Barnes-Hut algorithm has been shown to be an effective technique for reduction of the computational complexity and memory requirements in the capacitance extraction problem for general three-dimensional interconnects. In this paper we discuss the effect of the layered substrate on the Barnes-Hut clustering approximation using the half-space example. The modified formula for center-of-charge location in half-space is derived and validated.