Area penalty for sublinear signal propagation delay on chip

Sublinear signal propagation delay in VLSI circuits carries a far greater penalty in wire area than is commonly realized. Therefore, the global complexity of VLSI circuits is more layout dependent than previously thought. This effect will be truly pronounced in the emerging wafer scale integration technology. We establish lower bounds on the trade-off between sublinear signalling speed and layout area for the implementation of a complete binary tree in VLSI. In particular, sublinear delay can only be realized at the cost of superlinear area. Designs with equal length wires can either not be laid out at all, viz. for logarithmic delay, or require such long wires in the case of radical delay (i.e., rth root of the wire length) that the aimed for gain in speed is cancelled. Also for wire length distributions commonly occurring on chip it appears that the requirements for sublinear signal propagation delay tend to cancel the gain.