A 2-D Capacitance Solver with Finite Difference Method

In this paper, we present a capacitance solver based on finite difference method (FDM). It simulates the cross section of interconnect structures and computes the capacitances per unit length. The techniques of forming symmetric coefficient matrix and nonuniform FDM grids are developed. And, with a sparse direct solver based on Cholesky factorization the presented solver exhibits high runtime efficiency with good accuracy. Experiments on pattern structures show that the presented solver is 3X faster than Raphael rc2, and is capable of accurately extracting structures with trapezoidal cross-section conductors and conformal dielectrics.