Optimal linewidth distribution minimizing average signal delay for RC limited circuits

Based on idealized interconnect scaling rules, we derive the optimal distribution of linewidths as a function of length for wire-limited layouts utilizing RC-limited interconnections. We show that the width of the wires should be chosen proportional to the cube root of their length for two-dimensional layouts and proportional to the fourth root of their length for full three-dimensional layouts so as to minimize average signal delay.