On optimal tapering of FET chains in high-speed CMOS circuits

Transistor tapering is a technique applied to optimize the geometries of CMOS transistors in high-performance circuit design with a view to minimizing the delay of a FET network. Currently, in a long FET network where MOS devices are stacked over one another to form a series chain network, the dimensions of the transistors are decreased from the bottom transistor to the top transistor in a manner where the width of transistors is tapered linearly or exponentially. However, it has not been mathematically proved whether either of these tapering schemes yields optimal results in terms of minimization of switching delays of the network. We rigorously analyze MOS circuits consisting of long FET chains under the widely used Elmore delay model and derive the optimality of transistor tapering by employing variational calculus. We demonstrate that neither linear nor exponential tapering alone minimizes the discharge time of the FET chain. Instead, a composition of exponential and constant tapering actually optimizes the delay of the network. Both analytical and simulation results are always consistent.