Exact closed-form expressions for substrate resistance and capacitance extraction in nanoscale VLSI

A new exact formula to determine the substrate resistance and capacitance is presented in this work. It is derived from the solution of the Laplace equations for equivalent problems. It achieves the level of accuracy of standard electromagnetic methods while it is orders of magnitude faster than them. Equations for both rectangular and non-rectangular shapes of interconnect lines which apply to sub-micron technologies are presented. Both data from commercial simulators and measurement data obtained from a fabricated test chip are utilized in order to show the validity of the proposed formula. The results show that the proposed formula succeeds in computing the substrate's resistive and capacitive coupling.