Optimal Wire Shape with Consideration of Coupling Capacitance under Elmore Delay Model

In this paper, by using calculus of variations, we determine the op-timal shape for a wire under the Elmore delay model. Coupling capacitance has been taken into consideration explicitly by treat-ing it as another source of grounded capacitance. Given two wires in parallel, one has uniform width and the other has non-uniform width whose shape is described by a function f(x). Let T D be the delay through the non-uniform wire. We determine f(x) such that T D is minimized. We also extend our study to the case where a non-uniform wire has two neighboring wires. Our study shows that the optimal shape function satisfies an integral equation. Numer-ical methods are employed to solve the corresponding differential equation and carry out the integration. We provide an efficient al-gorithm to find the optimal solution. Experiments show that it only takes several iterations to get the optimal results by using our al-gorithm. Our experiments also show that the wire delay T D is a convex function of the wire width at the driver end. 1