Fast on-chip inductance extraction of VLSI including angled interconnects

A formula-based approach for extracting the inductance of on-chip VLSI interconnections is presented. All of the formulae have been previously proposed and are well-known, but the degrees of accuracy they provide in this context have not previously been examined. The accuracy of the equations for a 0.1 mum technology node is evaluated through comparison of their results with those of 3-D field solvers. Comprehensive evaluation has proven that the maximum relative error of self- and mutual inductances as calculated by the formulae are less than 5% for parallel wires and less than 13% for angled wires, when wire width is limited to no more than 10 times the minimum. When applied to a realistic example with 43 wire segments, a program using the formula-based approach extracts values more than 60 times faster than a 3-D field solver.