Fast multipole integral equation method for VLSI interconnect inductance calculation

In this paper, a modified fast multipole integral (FMI) method is proposed for the calculation of the frequency dependent inductance of on-chip interconnects. The method is based on the discretization of the integral formulations and the fast multipole method by which the magnetic vector potentials induced by the currents through the conductors were calculated at the cost of O (N), where N is the number of the conductor elements divided in the hierarchical manner. The numeral results of integrated circuit interconnect structures demonstrate that the new approach significantly improves the calculation speed and reduce the memory consumed as the number of on chip interconnects under analysis continuously goes up when the former filament-based inductance extraction algorithm, such as Fasthenry, is out of practice. And the self/mutual inductance extracted by the proposed method can also keep a good precision as shown in the numerical results.