Fast method to calculate the frequency-dependent resistance and inductance of interconnect in VLSI circuits

A simplified method is proposed for fast extraction of the frequency-dependent resistance R and inductance L of interconnect, by combining the cross-section coupled circuit method with the boundary element method (BEM). The coupled circuit method is used to calculate resistances and inductances in the low frequency range. The BEM solves the Laplace equation to obtain the capacitance matrix [C], which is then inverted to obtain the inductance matrix at high frequencies when only the current is distributed over the conductor surface. The analysis then calculates the resistance matrix from the inductance matrices by applying Wheeler's rule. A cubic spline interpolation between resistance and inductance at low and high frequencies gives good results over entire frequency range. The method avoids solving the coupled surface integral equation for the eddy current, the total calculational burden is greatly reduced. This method can be applied to most parasitic extraction problems in VLSI.