Shaping a VLSI wire to minimize delay using transmission line model

We consider continuous wire sizing optimization for non uniform wires. Our objective is to find the shape function of a wire which minimizes delay. This problem has been studied recently under the Elmore delay model (W.C. Elmore, 1948). However, it is well known that Elmore delay is only a rough estimate of the actual delay and thus more accurate models should be used to determine the wire shape function. Our study uses the transmission line model which gives a very accurate estimation of the actual delay. Since previous studies under Elmore delay model suggest that exponential wire shape is effective for delay minimization, we restrict the wire shape function to be of the form f(x)=ae/sup -bx/. By solving the diffusion equation, we derive the transient response in the time domain as a function of a and b for both step and ramp input. The coefficients a and b are then determined so that the actual delay (50% delay) is minimized. Our algorithm is very efficient; in all the experiments we performed, the wire shape functions can be determined in less than 1 second.